In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f...In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f(x)≠0,the system is non-Hamiltonian,so we have to introduce some reversibility assumptions to apply a suitable twist theorem,for reversible maps with small twist.Moreover,when the nonnegative parameterαdecreases to 0,the system becomes discontinuous.In this case,we need to introduce some suitable transformations to overcome the lack of regularity.We will prove that for any nonnegative parameterα,when p(t)is an odd periodic function satisfying∣∣∫2π0p(t)sintdift∣∣<4,all the solutions are bounded;when p(t)satisfies∣∣∫2π0p(t)sintdift∣∣>4,the SD oscillator has unbounded solutions,and when p(t)satisfies∣∣∫_(0)^(2π)p(t)sintdift∣∣≥4+|F|_(∞),all the solutions are unbounded.展开更多
In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="&q...In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup>n</sup> (n ≥ 1), where d<sub>1</sub> > 0, d<sub>2</sub> > 0 with parameter χ ∈ R. When d<sub>1</sub> = d<sub>2</sub> + χ, satisfying for all initial data 0 ≤ n<sub>0</sub> ∈ C<sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < v<sub>0</sub>∈ W<sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).展开更多
In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forci...In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.展开更多
We consider a class of nonlinear parabolic equations whose prototype is ut-Δu=b(x,t)·■+γ|■u|^(2)-divF(x,t)+f(x,t),(x,t)∈ΩT,u(x,t)=∈ГT,u(x,0)=u0(x),x∈Ω where the functions|b(x,t)|^(2),|F(x,t)|^(2),f(x,t)...We consider a class of nonlinear parabolic equations whose prototype is ut-Δu=b(x,t)·■+γ|■u|^(2)-divF(x,t)+f(x,t),(x,t)∈ΩT,u(x,t)=∈ГT,u(x,0)=u0(x),x∈Ω where the functions|b(x,t)|^(2),|F(x,t)|^(2),f(x,t)lie in the space Lr(0,T;Lq(Ω)),γis a positive constant.The purpose of this paper is to prove,under suitable assumptions on the integrability of the space Lr(0,T;Lq(Ω))for the source terms and the coefficient of the gradient term,a priori L^(∞)estimate and the existence of bounded solutions.The methods consist of constructing a family of perturbation problems by regularization,Stampacchia’s iterative technique fulfilled by an appropriate nonlinear test function and compactness argument for the limit process.展开更多
Using the notion of an isolated invariant set and an isolating block, an existence criterion of bifurcation points of nonstationary bounded solutions to ordinary differential systems depending on a parameter is given.
The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper...The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.展开更多
A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,the...A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.展开更多
The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results a...The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.展开更多
A piston problem of viscous polytropic gas equations is discussed. It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time, t...A piston problem of viscous polytropic gas equations is discussed. It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time, then there exists a periodic solution to the piston problem with the same period.展开更多
The boundedness is proved under more general structural conditions to solutions of elliptic variational inequalities and a priori estimates are obtained to maximum modulus of solutions for some special cases.
In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are...In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.展开更多
The topic on the subspaces for the polynomially or exponentially bounded weak mild solutions of the following abstract Cauchy problem d^2/（dr^2）u（t,x）=Au（t,x）;u（0,x）=x,d/（dt）u（0,x）=0,x∈X is studied, wher...The topic on the subspaces for the polynomially or exponentially bounded weak mild solutions of the following abstract Cauchy problem d^2/（dr^2）u（t,x）=Au（t,x）;u（0,x）=x,d/（dt）u（0,x）=0,x∈X is studied, where A is a closed operator on Banach space X. The case that the problem is ill-posed is treated, and two subspaces Y（A, k） and H（A, ω） are introduced. Y（A, k） is the set of all x in X for which the second order abstract differential equation has a weak mild solution v（ t, x） such that ess sup{（1＋t）^-k｜d/（dt）〈v（t,x）,x^＊〉｜：t≥0,x^＊∈X^＊,｜x^＊‖≤1}〈＋∞. H（A, ω） is the set of all x in X for which the second order abstract differential equation has a weak mild solution v（t,x）such that ess sup{e^-ωl｜d/（dt）〈v（t,x）,x^＊）｜：t≥0,x^＊∈X^＊,‖x^＊‖≤1}〈＋∞. The following conclusions are proved that Y（A, k） and H（A, ω） are Banach spaces, and both are continuously embedded in X; the restriction operator A ｜ Y（A,k） generates a once-integrated cosine operator family { C（t） }t≥0 such that limh→0＋^-1/h‖C（t＋h）-C（t）‖Y（A,k）≤M（1＋t）^k,arbitary t≥0; the restriction operator A ｜H（A,ω） generates a once- integrated cosine operator family {C（t）}t≥0 such that limh→0＋^-1/h‖C（t＋h）-C（t）‖H（A,ω）≤≤Me^ωt,arbitary t≥0.展开更多
We are concerned with the boundedness for the equation x″+f(x,x′)+ω^(2)x=p(t),where p is quasi-periodic function.Since the corresponding system is non-Hamiltonian,we transform the original system into a new reversi...We are concerned with the boundedness for the equation x″+f(x,x′)+ω^(2)x=p(t),where p is quasi-periodic function.Since the corresponding system is non-Hamiltonian,we transform the original system into a new reversible one,the Poincarémapping of which satisfies the twist theorem for quasi-periodic reversible mappings of low smoothness,or is close to its linear part by normal form theorem.We then obtain results concerning the boundedness of solutions based on the recently work.The above two cases need some smooth and growth assumptions for f and p,which are precisely the innovations of this paper.展开更多
In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s p...In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.展开更多
In this article, we study the existence of sign-changing solutions for the following SchrSdinger equation -△u ＋ λV（x）u = K（x）｜u｜^p-2u x∈R^N, u→0 as ｜x｜→ ＋∞, 2N where N ≥ 3, λ〉 0 is a parameter, 2 〈...In this article, we study the existence of sign-changing solutions for the following SchrSdinger equation -△u ＋ λV（x）u = K（x）｜u｜^p-2u x∈R^N, u→0 as ｜x｜→ ＋∞, 2N where N ≥ 3, λ〉 0 is a parameter, 2 〈 p 〈 2N/N-2, and the potentials V（x） and K（x） satisfy some suitable conditions. By using the method based on invariant sets of the descending flow, we obtain the existence of a positive ground state solution and a ground state sign-changing solution of the above equation for small λ, which is a complement of the results obtained by Wang and Zhou in [J. Math. Phys. 52, 113704, 2011].展开更多
Suction caisson foundation derives most of their uplift resistance from passive suction developed during the pullout movement. It was observed that the passive suction generated in soil at the bottom of the caisson an...Suction caisson foundation derives most of their uplift resistance from passive suction developed during the pullout movement. It was observed that the passive suction generated in soil at the bottom of the caisson and the failure mode of suction caisson foundation subjecting pullout loading behaves as a reverse compression failure mechanism.The upper bound theorems have been proved to be a powerful method to find the critical failure mechanism and critical load associated with foundations, buried caissons and other geotechnical structures. However, limited attempts have been reported to estimate the uplift bearing capacity of the suction caisson foundation using the upper bound solution. In this paper, both reverse failure mechanisms from Prandtl and Hill were adopted as the failure mechanisms for the computation of the uplift bearing capacity of the suction caisson. New equations were proposed based on both failure mechanisms to estimate the pullout capacity of the suction caisson. The proposed equations were verified by the test results and experimental data from published literature. And the two solutions agree reasonably well with the other test results. It can be proved that both failure mechanisms are reasonably and more consistent with the actual force condition.展开更多
The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian ...The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.展开更多
In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general in...In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.展开更多
In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞）, to a Lienard system with a time-dependent force. Since it is not a Hamiltonian syst...In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞）, to a Lienard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non- Hamiltonian form are overcome by applying the Schauder＇s fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Lienard system.展开更多
基金supported by the Key Research Funds for the Universities of Henan Province(No.19A110018)the Foundation for Key Teachers of Henan Polytechnic University(No.2022XQG-09)。
文摘In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f(x)≠0,the system is non-Hamiltonian,so we have to introduce some reversibility assumptions to apply a suitable twist theorem,for reversible maps with small twist.Moreover,when the nonnegative parameterαdecreases to 0,the system becomes discontinuous.In this case,we need to introduce some suitable transformations to overcome the lack of regularity.We will prove that for any nonnegative parameterα,when p(t)is an odd periodic function satisfying∣∣∫2π0p(t)sintdift∣∣<4,all the solutions are bounded;when p(t)satisfies∣∣∫2π0p(t)sintdift∣∣>4,the SD oscillator has unbounded solutions,and when p(t)satisfies∣∣∫_(0)^(2π)p(t)sintdift∣∣≥4+|F|_(∞),all the solutions are unbounded.
文摘In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup>n</sup> (n ≥ 1), where d<sub>1</sub> > 0, d<sub>2</sub> > 0 with parameter χ ∈ R. When d<sub>1</sub> = d<sub>2</sub> + χ, satisfying for all initial data 0 ≤ n<sub>0</sub> ∈ C<sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < v<sub>0</sub>∈ W<sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).
基金Supported by Key Research Funds for the Universities of Henan Province(Grant No.19A110018)Foundation for Key Teacher of Henan Polytechnic University(Grant No.2022XQG-09).
文摘In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.
基金Supported by the National Natural Science Foundation of China(Grant No.11901131)the University-Level Research Fund Project in Guizhou University of Finance and Economics(Grant No.2019XYB08)。
文摘We consider a class of nonlinear parabolic equations whose prototype is ut-Δu=b(x,t)·■+γ|■u|^(2)-divF(x,t)+f(x,t),(x,t)∈ΩT,u(x,t)=∈ГT,u(x,0)=u0(x),x∈Ω where the functions|b(x,t)|^(2),|F(x,t)|^(2),f(x,t)lie in the space Lr(0,T;Lq(Ω)),γis a positive constant.The purpose of this paper is to prove,under suitable assumptions on the integrability of the space Lr(0,T;Lq(Ω))for the source terms and the coefficient of the gradient term,a priori L^(∞)estimate and the existence of bounded solutions.The methods consist of constructing a family of perturbation problems by regularization,Stampacchia’s iterative technique fulfilled by an appropriate nonlinear test function and compactness argument for the limit process.
基金supported by the National Natural Science Foundation of China(No.10871181)
文摘Using the notion of an isolated invariant set and an isolating block, an existence criterion of bifurcation points of nonstationary bounded solutions to ordinary differential systems depending on a parameter is given.
基金Supported by the National Natural Science Foundation of China(10771171)Supported by the 555 Innovation Talent Project of Gansu Province(GS-555-CXRC)+1 种基金Supported by the Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212)Supported by the Youth Foundation of Dingxi Advanced Teachers College(1333)
文摘The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.
文摘A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.
基金The NSF (10271095) of China and NWNU-KJCXGC-212.
文摘The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.
文摘A piston problem of viscous polytropic gas equations is discussed. It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time, then there exists a periodic solution to the piston problem with the same period.
文摘The boundedness is proved under more general structural conditions to solutions of elliptic variational inequalities and a priori estimates are obtained to maximum modulus of solutions for some special cases.
基金supported by the NSFC (12071438)supported by the NSFC (12201232)
文摘In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.
基金The Natural Science Foundation of Department ofEducation of Jiangsu Province (No06KJD110087)
文摘The topic on the subspaces for the polynomially or exponentially bounded weak mild solutions of the following abstract Cauchy problem d^2/（dr^2）u（t,x）=Au（t,x）;u（0,x）=x,d/（dt）u（0,x）=0,x∈X is studied, where A is a closed operator on Banach space X. The case that the problem is ill-posed is treated, and two subspaces Y（A, k） and H（A, ω） are introduced. Y（A, k） is the set of all x in X for which the second order abstract differential equation has a weak mild solution v（ t, x） such that ess sup{（1＋t）^-k｜d/（dt）〈v（t,x）,x^＊〉｜：t≥0,x^＊∈X^＊,｜x^＊‖≤1}〈＋∞. H（A, ω） is the set of all x in X for which the second order abstract differential equation has a weak mild solution v（t,x）such that ess sup{e^-ωl｜d/（dt）〈v（t,x）,x^＊）｜：t≥0,x^＊∈X^＊,‖x^＊‖≤1}〈＋∞. The following conclusions are proved that Y（A, k） and H（A, ω） are Banach spaces, and both are continuously embedded in X; the restriction operator A ｜ Y（A,k） generates a once-integrated cosine operator family { C（t） }t≥0 such that limh→0＋^-1/h‖C（t＋h）-C（t）‖Y（A,k）≤M（1＋t）^k,arbitary t≥0; the restriction operator A ｜H（A,ω） generates a once- integrated cosine operator family {C（t）}t≥0 such that limh→0＋^-1/h‖C（t＋h）-C（t）‖H（A,ω）≤≤Me^ωt,arbitary t≥0.
基金Supported by the NSFC(Grant No.11971059)the Fundamental Research Funds for the Central Universities(Grant No.202261096)+2 种基金the NSFC(Grant No.11971059)the NSFC(Grant No.12201587)the Shandong Provincial Natural Science Foundation,China(Grant No.A010704)。
文摘We are concerned with the boundedness for the equation x″+f(x,x′)+ω^(2)x=p(t),where p is quasi-periodic function.Since the corresponding system is non-Hamiltonian,we transform the original system into a new reversible one,the Poincarémapping of which satisfies the twist theorem for quasi-periodic reversible mappings of low smoothness,or is close to its linear part by normal form theorem.We then obtain results concerning the boundedness of solutions based on the recently work.The above two cases need some smooth and growth assumptions for f and p,which are precisely the innovations of this paper.
文摘In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.
基金supported by the Fundamental Research Funds for the Central Universities(2014QNA67)
文摘In this article, we study the existence of sign-changing solutions for the following SchrSdinger equation -△u ＋ λV（x）u = K（x）｜u｜^p-2u x∈R^N, u→0 as ｜x｜→ ＋∞, 2N where N ≥ 3, λ〉 0 is a parameter, 2 〈 p 〈 2N/N-2, and the potentials V（x） and K（x） satisfy some suitable conditions. By using the method based on invariant sets of the descending flow, we obtain the existence of a positive ground state solution and a ground state sign-changing solution of the above equation for small λ, which is a complement of the results obtained by Wang and Zhou in [J. Math. Phys. 52, 113704, 2011].
基金financially supported by the National Key Research and Development Program(Grant No.2017YFC0703408)the National Natural Science Foundation of China(Grant Nos.51678145 and 51878160)
文摘Suction caisson foundation derives most of their uplift resistance from passive suction developed during the pullout movement. It was observed that the passive suction generated in soil at the bottom of the caisson and the failure mode of suction caisson foundation subjecting pullout loading behaves as a reverse compression failure mechanism.The upper bound theorems have been proved to be a powerful method to find the critical failure mechanism and critical load associated with foundations, buried caissons and other geotechnical structures. However, limited attempts have been reported to estimate the uplift bearing capacity of the suction caisson foundation using the upper bound solution. In this paper, both reverse failure mechanisms from Prandtl and Hill were adopted as the failure mechanisms for the computation of the uplift bearing capacity of the suction caisson. New equations were proposed based on both failure mechanisms to estimate the pullout capacity of the suction caisson. The proposed equations were verified by the test results and experimental data from published literature. And the two solutions agree reasonably well with the other test results. It can be proved that both failure mechanisms are reasonably and more consistent with the actual force condition.
基金The National Natural Science Foundation of China(No.11371089)the China Postdoctoral Science Foundation(No.2016M601688)
文摘The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.
文摘In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.
文摘In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞）, to a Lienard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non- Hamiltonian form are overcome by applying the Schauder＇s fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Lienard system.
