In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome...In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differ...AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differentiation, cell cycle control and the expression of house-keeping genes, and further to search for markers which could be used in guiding the pathological diagnosis of three lesions. METHODS: Expressions of MUC5AC, MUC6, adenomatous polyposis coli (APC), p53, Ki-67, proliferation cell nuclear antigen (PCNA) and EGFR were studied by immunohistochemistry with a standard Envision technique in formalinfixed and paraffin-embedded specimens from 43 RH, 35 IDys, 35 Dys and 36 intestinal type gastric carcinomas (IGC). In addition, Bayes discriminant analysis was used to investigate the value of markers studied in differential diagnosis of RH, IDys, Dys and IGC. RESULTS: The MUC5AC and MUC6 antigen expressions in RH, IDys, Dys and IGC decreased gradually (MUC5AC:86.04%, 77.14%, 28.57%, 6.67%; MUC6: 65.15%, 54.29%, 20.00%, 25.00%, respectively). The expressions of the two markers had no significant difference between RH and IDys, but were all significantly higher than those ofthe other two lesions (MUC5AC: x2 = 27.607, 38.027 and 17.33, 26.092; MUC6: x2= 16.54, 12.665 and 9.282, 6.737, P＜0.01). There was no significant differencebetween RH and IDys, Dys and IGC in MUC6 expression. The APC gene expression in the four lesions had a similar decreasing tendency (RH 69.76%, IDys 68.57%, Dys39.39%, IGC 22.86%), and it was significantly higher in the first two lesions than in the last two (x2 = 7.011,16.995 and 14.737, 19.817, P＜0.05). The p53 expressionin RH, IDys, Dys and IGC was 6.98%, 20%, 57.14% and 50%, respectively. There was no significant differencebetween RH and IDys or Dys and IGC, but the p53 expression in RH and IDys was significantly lower than that in Dys and IGC (x2 = 7.011, 16.995 and 14.737, 19.817, P＜0.01).The Ki-67 label index was significantly different among four lesions (RH: 0.298±8.92%, IDys: 0.358±9.25%,Dys: 0.498±9.03%, IGC: 0.620±10.8%, P＜0.001). Positive immunostaining of PCNA was though observed in all specimens, significant differences were detected among four lesions (F= 95.318, P＜0.01). In addition, we used Bayes discriminant analysis to investigate molecular pathological classification of the lesions, and obtained the best result with the combination of MUC5AC, Ki-67 and PCNA. The overall rate of correct classification was67.4% (RH), 68.6% (IDys), 70.6% (Dys) and 84.8% (IGC), respectively.CONCLUSION: Dys has neoplastic biological characteristics, while RH and IDys display hyperplastic characteristics. MUC5AC and proliferation-related biomarkers (Ki-67, PCNA) are more specific in distinguishing Dys from RH and IDys.展开更多
In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
AIM To evaluate the usefulness of frozen section diagnosis(FSD) of bile duct margins during surgery for extrahepatic cholangiocarcinoma(CCA). METHODS We retrospectively analyzed 74 consecutive patients who underwent s...AIM To evaluate the usefulness of frozen section diagnosis(FSD) of bile duct margins during surgery for extrahepatic cholangiocarcinoma(CCA). METHODS We retrospectively analyzed 74 consecutive patients who underwent surgery for extrahepatic CCA from 2012 to 2017, during which FSD of bile duct margins was performed. They consisted of 40 distant and 34 perihilar CCAs(45 and 55 bile duct margins, respectively). The diagnosis was classified into three categories: negative, borderline(biliary intraepithelial neoplasia-1 and 2, and indefinite for neoplasia), or positive. FSD in the epithelial layer, subepithelial layer, and total layer was compared with corresponding permanent section diagnosis(PSD) postoperatively.Then, association between FSD and local recurrence was analyzed with special reference to borderline.RESULTS Analysis of 100 duct margins revealed that concordance rate between FSD and PSD was 68.0% in the total layer, 69.0% in the epithelial layer, and 98.0% in the subepithelial layer. The extent of remaining biliary epithelium was comparable between FSD and PSD, and more than half of the margins lost > 50% of the entire epithelium, suggesting low quality of the samples. In FSD, the rate of negative margins decreased and that of borderline and positive margins increased according to the extent of the remaining epithelium. Diagnostic discordance between FSD and PSD was observed in 31 epithelial layers and two subepithelial layers. Alteration from borderline to negative was the most frequent(20 of the 31 epithelial layers). Patients with positive margin in the total and epithelial layers by FSD demonstrated a significantly worse local recurrence-free survival(RFS) compared with patients with borderline and negative margins, which revealed comparable local RFS. Patients with borderline and negative margins in the epithelial layer by PSD also revealed comparable local RFS. These results suggested that epithelial borderline might be regarded substantially as negative. When classifying the status of the epithelial layer either as negative or positive, concordance rates between FSD and PSD in the total, epithelial, and subepithelial layers were 95.0%, 93.0%, and 98.0%, respectively.CONCLUSION During intraoperative assessment of bile duct margin, borderline in the epithelial layer can be substantially regarded as negative, under which condition FSD is comparable to PSD.展开更多
We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute t...We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.展开更多
This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefin...This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality （LMI）. Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.展开更多
In this article, the authors investigate the existence problem for Hardy Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities.
This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solution...This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.展开更多
The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficul...The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficult to solve the equation using the current method. In this paper, it prov ides a simple method by discussing the structure of solution based on the theory of free abelian group. In addition, this method makes it easy to get the genera lized solution of the equation using the computer.展开更多
In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" ...In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.展开更多
We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and...We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and indefinite weight function, we prove the existence and uniqueness of solutions which are positive in both u and v and asymptotically stable corresponding to the case where the populations can co-exist.展开更多
In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is pr...In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H<sup>1</sup>-condition number of preconditioned operator B<sub>h</sub><sup>-1</sup>A<sub>h</sub> is uniformly bounded and its B<sub>h</sub>-singular values cluster in a positive finite interval, where A<sub>h</sub> is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, B<sub>h</sub> is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of B<sub>h</sub><sup>-1</sup> is given.展开更多
In this article, we construct some spacelike austere submanifolds in pseduoEuclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere subma...In this article, we construct some spacelike austere submanifolds in pseduoEuclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces.展开更多
The quantum effect plays an important role in quantum thermodynamics,and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention.Based on two trapped ions,we propo...The quantum effect plays an important role in quantum thermodynamics,and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention.Based on two trapped ions,we propose a scheme to add an indefinite causal order to the isochoric cooling stroke of an Otto engine through reservoir engineering.Then,we observe that the quasi-static efficiency of this heat engine is far beyond the efficiency of a normal Otto heat engine and may reach one.When the power is its maximum,the efficiency is also much higher than that of a normal Otto heat engine.This enhancement may originate from the nonequilibrium of the reservoir and the measurement on the control qubit.展开更多
We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavio...We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).展开更多
In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spe...In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.展开更多
In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especi...In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.展开更多
In this paper, we investigate nonlinear Hamiltonian elliptic system {-△u＋b（x）· u＋（V（x）＋τ）u=K（x）g（v） in R^N,-△u-b（x）· v＋（V（x）＋τ）v=K（x）f（u） in R^N,u（x）→ and v（x）→0 as ｜x｜...In this paper, we investigate nonlinear Hamiltonian elliptic system {-△u＋b（x）· u＋（V（x）＋τ）u=K（x）g（v） in R^N,-△u-b（x）· v＋（V（x）＋τ）v=K（x）f（u） in R^N,u（x）→ and v（x）→0 as ｜x｜→∞2,where N ≥ 3, τ 〉 0 is a positive parameter and V, K are nonnegative continuous functions,f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing avariational setting, the existence of ground state solutions is obtained.展开更多
基金supported by the NSFC(11301297)the Hubei Provincial Natural Science Foundation of China(2024AFB730)+3 种基金the Yichang City Natural Science Foundation(A-24-3-008)the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(NAA2024ORG003)Gu's research was supported by the Zhejiang Provincial Natural Science Foundation(LQ21A010014)the NFSC(12101577).
文摘In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金Supported by the National Key Fundamental Research Project,No.G1998051203
文摘AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differentiation, cell cycle control and the expression of house-keeping genes, and further to search for markers which could be used in guiding the pathological diagnosis of three lesions. METHODS: Expressions of MUC5AC, MUC6, adenomatous polyposis coli (APC), p53, Ki-67, proliferation cell nuclear antigen (PCNA) and EGFR were studied by immunohistochemistry with a standard Envision technique in formalinfixed and paraffin-embedded specimens from 43 RH, 35 IDys, 35 Dys and 36 intestinal type gastric carcinomas (IGC). In addition, Bayes discriminant analysis was used to investigate the value of markers studied in differential diagnosis of RH, IDys, Dys and IGC. RESULTS: The MUC5AC and MUC6 antigen expressions in RH, IDys, Dys and IGC decreased gradually (MUC5AC:86.04%, 77.14%, 28.57%, 6.67%; MUC6: 65.15%, 54.29%, 20.00%, 25.00%, respectively). The expressions of the two markers had no significant difference between RH and IDys, but were all significantly higher than those ofthe other two lesions (MUC5AC: x2 = 27.607, 38.027 and 17.33, 26.092; MUC6: x2= 16.54, 12.665 and 9.282, 6.737, P＜0.01). There was no significant differencebetween RH and IDys, Dys and IGC in MUC6 expression. The APC gene expression in the four lesions had a similar decreasing tendency (RH 69.76%, IDys 68.57%, Dys39.39%, IGC 22.86%), and it was significantly higher in the first two lesions than in the last two (x2 = 7.011,16.995 and 14.737, 19.817, P＜0.05). The p53 expressionin RH, IDys, Dys and IGC was 6.98%, 20%, 57.14% and 50%, respectively. There was no significant differencebetween RH and IDys or Dys and IGC, but the p53 expression in RH and IDys was significantly lower than that in Dys and IGC (x2 = 7.011, 16.995 and 14.737, 19.817, P＜0.01).The Ki-67 label index was significantly different among four lesions (RH: 0.298±8.92%, IDys: 0.358±9.25%,Dys: 0.498±9.03%, IGC: 0.620±10.8%, P＜0.001). Positive immunostaining of PCNA was though observed in all specimens, significant differences were detected among four lesions (F= 95.318, P＜0.01). In addition, we used Bayes discriminant analysis to investigate molecular pathological classification of the lesions, and obtained the best result with the combination of MUC5AC, Ki-67 and PCNA. The overall rate of correct classification was67.4% (RH), 68.6% (IDys), 70.6% (Dys) and 84.8% (IGC), respectively.CONCLUSION: Dys has neoplastic biological characteristics, while RH and IDys display hyperplastic characteristics. MUC5AC and proliferation-related biomarkers (Ki-67, PCNA) are more specific in distinguishing Dys from RH and IDys.
文摘In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.
基金JSPS KAKENHI(No.JP16K08695)from the Ministry of Education,Culture,Sports,Science and Technology of Japan
文摘AIM To evaluate the usefulness of frozen section diagnosis(FSD) of bile duct margins during surgery for extrahepatic cholangiocarcinoma(CCA). METHODS We retrospectively analyzed 74 consecutive patients who underwent surgery for extrahepatic CCA from 2012 to 2017, during which FSD of bile duct margins was performed. They consisted of 40 distant and 34 perihilar CCAs(45 and 55 bile duct margins, respectively). The diagnosis was classified into three categories: negative, borderline(biliary intraepithelial neoplasia-1 and 2, and indefinite for neoplasia), or positive. FSD in the epithelial layer, subepithelial layer, and total layer was compared with corresponding permanent section diagnosis(PSD) postoperatively.Then, association between FSD and local recurrence was analyzed with special reference to borderline.RESULTS Analysis of 100 duct margins revealed that concordance rate between FSD and PSD was 68.0% in the total layer, 69.0% in the epithelial layer, and 98.0% in the subepithelial layer. The extent of remaining biliary epithelium was comparable between FSD and PSD, and more than half of the margins lost > 50% of the entire epithelium, suggesting low quality of the samples. In FSD, the rate of negative margins decreased and that of borderline and positive margins increased according to the extent of the remaining epithelium. Diagnostic discordance between FSD and PSD was observed in 31 epithelial layers and two subepithelial layers. Alteration from borderline to negative was the most frequent(20 of the 31 epithelial layers). Patients with positive margin in the total and epithelial layers by FSD demonstrated a significantly worse local recurrence-free survival(RFS) compared with patients with borderline and negative margins, which revealed comparable local RFS. Patients with borderline and negative margins in the epithelial layer by PSD also revealed comparable local RFS. These results suggested that epithelial borderline might be regarded substantially as negative. When classifying the status of the epithelial layer either as negative or positive, concordance rates between FSD and PSD in the total, epithelial, and subepithelial layers were 95.0%, 93.0%, and 98.0%, respectively.CONCLUSION During intraoperative assessment of bile duct margin, borderline in the epithelial layer can be substantially regarded as negative, under which condition FSD is comparable to PSD.
文摘We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.
基金supported by the National Natural Science Foundation of China(Nos.61174078,61170054,61402265)the Research Fund for the Taishan Scholar Project of Shandong Province of China
文摘This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality （LMI）. Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.
文摘In this article, the authors investigate the existence problem for Hardy Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities.
基金supported by the Hunan Provincial Innovation Foundation for Postgraduate(CX2013A003)the NNSF(11171351,11361078)SRFDP(20120162110021)of China
文摘This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.
文摘The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficult to solve the equation using the current method. In this paper, it prov ides a simple method by discussing the structure of solution based on the theory of free abelian group. In addition, this method makes it easy to get the genera lized solution of the equation using the computer.
文摘In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.
文摘We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and indefinite weight function, we prove the existence and uniqueness of solutions which are positive in both u and v and asymptotically stable corresponding to the case where the populations can co-exist.
基金The research was supported by the Doctoral Foundation of China Universitiesthe National Natural Science Foundation of China.
文摘In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H<sup>1</sup>-condition number of preconditioned operator B<sub>h</sub><sup>-1</sup>A<sub>h</sub> is uniformly bounded and its B<sub>h</sub>-singular values cluster in a positive finite interval, where A<sub>h</sub> is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, B<sub>h</sub> is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of B<sub>h</sub><sup>-1</sup> is given.
基金Supported by NSFC (10971029)NSFC-NSF(1081112053)supported by NSFC-Tian Yuan Fund (11026062)
文摘In this article, we construct some spacelike austere submanifolds in pseduoEuclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces.
基金supported by National Natural Science Foundation of China under Grant No.11965012Yunan Province’s Hi-tech Talents Recruitment Plan No.YNWR-QNBJ-2019-245。
文摘The quantum effect plays an important role in quantum thermodynamics,and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention.Based on two trapped ions,we propose a scheme to add an indefinite causal order to the isochoric cooling stroke of an Otto engine through reservoir engineering.Then,we observe that the quasi-static efficiency of this heat engine is far beyond the efficiency of a normal Otto heat engine and may reach one.When the power is its maximum,the efficiency is also much higher than that of a normal Otto heat engine.This enhancement may originate from the nonequilibrium of the reservoir and the measurement on the control qubit.
基金supported by Piano della Ricerca di Ateneo 2020-2022-PIACERIProject MO.S.A.I.C"Monitoraggio satellitare,modellazioni matematiche e soluzioni architettoniche e urbane per lo studio,la previsione e la mitigazione delle isole di calore urbano",Project EEEP&DLaD.S。
文摘We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).
基金Supported by the National Natural Science Foundation of China(11171152)the Jiangsu Natural Science Foundation of China(BK2010489)
文摘In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.
基金The Science and Technology Program(20110035) of Shanghai Maritime University
文摘In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.
基金partially supported by the Honghe University Doctoral Research Program(XJ17B11)Yunnan Province Applied Basic Research for Youthsthe Yunnan Province Local University(Part)Basic Research Joint Project(2017FH001-013)
文摘In this paper, we investigate nonlinear Hamiltonian elliptic system {-△u＋b（x）· u＋（V（x）＋τ）u=K（x）g（v） in R^N,-△u-b（x）· v＋（V（x）＋τ）v=K（x）f（u） in R^N,u（x）→ and v（x）→0 as ｜x｜→∞2,where N ≥ 3, τ 〉 0 is a positive parameter and V, K are nonnegative continuous functions,f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing avariational setting, the existence of ground state solutions is obtained.
