We study a class of nonlinear parabolic equations of the type：δb（u）/δt-div（a（x,t,u）△u）＋y（u）｜△u｜^2=f,where the right hand side belongs to L^1（Q）, b is a strictly increasing C^1-function and -div（a（x...We study a class of nonlinear parabolic equations of the type：δb（u）/δt-div（a（x,t,u）△u）＋y（u）｜△u｜^2=f,where the right hand side belongs to L^1（Q）, b is a strictly increasing C^1-function and -div（a（x, t, u）△u） is a Leray-Lions operator. The function g is just assumed to be continuous on R and to satisfy a sign condition. Without any additional growth assumption on u, we prove the existence of a renormalized solution.展开更多
In this paper, we establish the existence of the minimal Lp （p 〉 1） solution of backward stochastic differential equations （BSDEs） where the time horizon may be finite or infinite and the generators have a non-un...In this paper, we establish the existence of the minimal Lp （p 〉 1） solution of backward stochastic differential equations （BSDEs） where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {（Yn, Zn）} which is a Cauchy sequence in Sp × Mp space, and finally we prove {（Yn, Zn）} converges to the Lp （p 〉 1） solution of BSDEs.展开更多
An analytical solution for scattering of plane P waves by circular-arc layered alluvial valleys was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of alluvia...An analytical solution for scattering of plane P waves by circular-arc layered alluvial valleys was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of alluvial sequence and their relative stiffness on the scattering of incident waves.展开更多
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution...The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.展开更多
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e...The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.展开更多
Although common calcium-containing minerals such as calcite and gypsum may fix arsenic, the interaction between modified calcic minerals and arsenic has seldom been reported. The uptake behavior of As(Ⅲ)/As(V) from a...Although common calcium-containing minerals such as calcite and gypsum may fix arsenic, the interaction between modified calcic minerals and arsenic has seldom been reported. The uptake behavior of As(Ⅲ)/As(V) from aqueous solutions by calcium sulfate whisker(CSW, dihydrate or anhydrite) synthesized through a cooling recrystallization method was explored. A series of batch experiments were conducted to examine the effect of p H, reaction time, whisker dosage, and initial As concentration. X-ray diffraction(XRD) and scanning electron microscopy(SEM) were used to characterize the samples prepared. The results showed that p H of the aqueous solution was an important parameter for As(Ⅲ)/As(V) uptake, and an excellent removal efficiency could be achieved under strongly alkaline condition. The data from batch experiments for reaction of As(V) with calcium sulfate dihydrate whisker(CSDW) and calcium sulfate anhydrous whisker(CSAW) were well described with extended Langmuir EXT1 model, from which theoretic maximum adsorption capacity of 46.57 mg As(V)·(g CSDW)-1and 39.18 mg As(V)·(g CSAW)-1were obtained. Some calcium arsenate solids products,such as Ca As O3(OH)(weilite, syn), Ca3(As O4)2(calcium arsenate), Ca O–As2O5, Ca–As–O, Ca5(As O4)3OH·x H2O(calcium arsenate hydroxide hydrate), and Ca H(As O4)·2H2O(hydrogen calcium arsenic oxide hydrate), were detected at p H = 12.5 through XRD analysis. This indicates that the interaction mechanism between As(V) and CSW is a complex adsorption process combined with surface dissolution and chemical precipitation.展开更多
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p＆q-Laplacian type involving the critical Sobolev exponent：{-△pu-△qu=│u│^p＊-2u＋μ│u│^r-2u in Ω u...In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p＆q-Laplacian type involving the critical Sobolev exponent：{-△pu-△qu=│u│^p＊-2u＋μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^＊=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ （0, μ0）, the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.展开更多
An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The ...An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.展开更多
We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally L...We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.展开更多
A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities signifi...A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.展开更多
In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for ...In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.展开更多
The electrical conductance of 0.025 mol NaCl solution was measured at0.25-3.75 GPa and 20-370℃. As shown by the results, the conductance increases with temper-ature, and there is a liner relation between the reciproc...The electrical conductance of 0.025 mol NaCl solution was measured at0.25-3.75 GPa and 20-370℃. As shown by the results, the conductance increases with temper-ature, and there is a liner relation between the reciprocal of temperature and the logarithm ofthe conductance but their slopes are different at different pressures. The relations between theconductance and pressure is rather complex and there are some discontinuities: in the range of2.25-3.75 GPa, the conductance increases with the pressure; in the range of 1.25-2.0 GPa, theconductance is not related to the pressure; and at a pressure of 0.75 GPa, the conductance ishigher than that at the pressures nearby. This reflects that the NaCl solution has rather differentproperties of electronic chemistry at various pressures, and probably is an important cause forthe existence of the layers with high electrical conductance and low velocity in the Earth's crustand mantle.展开更多
In this paper,we consider the existence of multiple positive solutions of the following inhomepeneous semilinear elliptic equation where λ> 0.ed and ω is a bounded smooth open set in R2,h(x)∈ L 2(Ω),h(x) 0.f(t)...In this paper,we consider the existence of multiple positive solutions of the following inhomepeneous semilinear elliptic equation where λ> 0.ed and ω is a bounded smooth open set in R2,h(x)∈ L 2(Ω),h(x) 0.f(t)∈ C1([0.+∝)) satisfies f(0) =f'(0)=0.fn(t) exists and fn(t)> 0.0<f(t) <Cexp(at) for some constants C,α> 0.0 <u <2 and t∈(0.+c),f(t)<0tf'(t) for someθ ∈(0,1). By looking for the local miaimum of the corresponding energy functional we tain the first minimum positive solution and by applying mountain pass lemma around the ndboum positive solution we prove the following result:展开更多
The solvability of one dimensional fourth-order p-Laplace equations of the type [GRAPHICS] where, g(v) \ v \ (p-2) v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity ...The solvability of one dimensional fourth-order p-Laplace equations of the type [GRAPHICS] where, g(v) \ v \ (p-2) v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form f at zero and at infinity.展开更多
We establish some results on the existence of multiple nontrivial solutions for a class of p(x)-Lap-lacian elliptic equations without assumptions that the domain is bounded. The main tools used in the proof are the va...We establish some results on the existence of multiple nontrivial solutions for a class of p(x)-Lap-lacian elliptic equations without assumptions that the domain is bounded. The main tools used in the proof are the variable exponent theory of generalized Lebesgue-Sobolev spaces, variational methods and a variant of the Mountain Pass Lemma.展开更多
Let Ω be a smooth bounded domain in R^n. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation --△pu = ｜u｜^q-1 u ＋ λf（x） on Ω, and identify necessary and ...Let Ω be a smooth bounded domain in R^n. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation --△pu = ｜u｜^q-1 u ＋ λf（x） on Ω, and identify necessary and sufficient conditions on Ω and f（x） which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.展开更多
For a highly efficient recycling of a wastewater containing a high concentration of MgCl_(2),Al(Ⅲ)and P507 were scheduled to be removed in advance.In this study,the in-situ removal of Al(Ⅲ)and P507 from a high conce...For a highly efficient recycling of a wastewater containing a high concentration of MgCl_(2),Al(Ⅲ)and P507 were scheduled to be removed in advance.In this study,the in-situ removal of Al(Ⅲ)and P507 from a high concentration MgCl_(2)solution at different pH values and Al/P molar ratios was investigated.The results showed that P507 formed organic complexes of Al_(x)(OH)_y^(Z+)-P507 at pH of 2.0-4.0.At pH of 4.0-5.0,Al(Ⅲ)precipitated and transferred into Al(OH)_(3)with a flocculent amorphous morphology.Active sites on the Al(OH)_(3)surface enhanced the removal efficiency of P507.At pH of 6.0-6.5,Al(Ⅲ)and Mg(Ⅱ)formed layered crystalline Al(OH)_(3)and MgAl_(2)(OH)_(8with)small pore channels and fewer active sites,resulting in a reduced removal efficiency of P507.When the Al/P molar ratio exceeded 13 and the pH was between 4.0 and 5.0,the removal rates of both Al(Ⅲ)and P507 were higher than98%,while the concentration loss of Mg(Ⅱ)was only 0.2%-0.9%.展开更多
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
文摘We study a class of nonlinear parabolic equations of the type：δb（u）/δt-div（a（x,t,u）△u）＋y（u）｜△u｜^2=f,where the right hand side belongs to L^1（Q）, b is a strictly increasing C^1-function and -div（a（x, t, u）△u） is a Leray-Lions operator. The function g is just assumed to be continuous on R and to satisfy a sign condition. Without any additional growth assumption on u, we prove the existence of a renormalized solution.
基金Supported by the National Natural Science Foundation of China(Grant No.11371362)the Fundamental Research Funds for the Central Universities(Grant No.2012LWB48)
文摘In this paper, we establish the existence of the minimal Lp （p 〉 1） solution of backward stochastic differential equations （BSDEs） where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {（Yn, Zn）} which is a Cauchy sequence in Sp × Mp space, and finally we prove {（Yn, Zn）} converges to the Lp （p 〉 1） solution of BSDEs.
基金State Natural Science Foundation of China (No.59878032).
文摘An analytical solution for scattering of plane P waves by circular-arc layered alluvial valleys was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of alluvial sequence and their relative stiffness on the scattering of incident waves.
文摘The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.
文摘The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.
基金Supported by the Science and Technology Plan Project of Hunan Province(2013FJ3034)the Open Foundation of the Innovation Platform in Higher Education of Hunan Province(12K051)the programs of Xiangtan University(2011XZX12,2010QDZ37)
文摘Although common calcium-containing minerals such as calcite and gypsum may fix arsenic, the interaction between modified calcic minerals and arsenic has seldom been reported. The uptake behavior of As(Ⅲ)/As(V) from aqueous solutions by calcium sulfate whisker(CSW, dihydrate or anhydrite) synthesized through a cooling recrystallization method was explored. A series of batch experiments were conducted to examine the effect of p H, reaction time, whisker dosage, and initial As concentration. X-ray diffraction(XRD) and scanning electron microscopy(SEM) were used to characterize the samples prepared. The results showed that p H of the aqueous solution was an important parameter for As(Ⅲ)/As(V) uptake, and an excellent removal efficiency could be achieved under strongly alkaline condition. The data from batch experiments for reaction of As(V) with calcium sulfate dihydrate whisker(CSDW) and calcium sulfate anhydrous whisker(CSAW) were well described with extended Langmuir EXT1 model, from which theoretic maximum adsorption capacity of 46.57 mg As(V)·(g CSDW)-1and 39.18 mg As(V)·(g CSAW)-1were obtained. Some calcium arsenate solids products,such as Ca As O3(OH)(weilite, syn), Ca3(As O4)2(calcium arsenate), Ca O–As2O5, Ca–As–O, Ca5(As O4)3OH·x H2O(calcium arsenate hydroxide hydrate), and Ca H(As O4)·2H2O(hydrogen calcium arsenic oxide hydrate), were detected at p H = 12.5 through XRD analysis. This indicates that the interaction mechanism between As(V) and CSW is a complex adsorption process combined with surface dissolution and chemical precipitation.
基金Supported by NSFC (10571069 and 10631030) the Lap of Mathematical Sciences, CCNU, Hubei Province, China
文摘In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p＆q-Laplacian type involving the critical Sobolev exponent：{-△pu-△qu=│u│^p＊-2u＋μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^＊=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ （0, μ0）, the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.
基金National Natural Science Foundation of China Under Grant No.50378063Excellent Young Teacher Program of Ministry of Education
文摘An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.
基金supported by the National Science Foundation of China (11001063, 10971043)the Fundamental Research Funds for the Central Universities (HEUCF 20111134)+2 种基金China Postdoctoral Science Foundation Funded Project (20110491032)Heilongjiang Provincial Science Foundation for Distinguished Young Scholars (JC200810)Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (A200803)
文摘We study a nonlinear periodic problem driven by the p（t）-Laplacian and having a nonsmooth potential （hemivariational inequalities）. Using a variational method based on nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of at least two nontrivial solutions under the generalized subquadratic and then establish the existence of at least one nontrivial solution under the generalized superquadratic.
基金Supported by National Natural Science Foundation of China (50378063), Excellent Young Teachers Program of MOE and SRF for ROCS, MOE.
文摘A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.
基金supported by the Zhejiang Natural Science Foundation of China(LQ13A010022)supported by the Qianjiang professorship of Zhejiang Province of Chinathe National Natural Science Foundation of China(11271105)
文摘In this article, we study the global L^∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ=3, we apply for the maximum principle to obtain the L^∞ estimates w(ρ^δ,ε, u^δ,ε)≤ B(t) and z(ρ^δ,ε, u^δ,ε)≤ B(t) for the viscosity solutions (ρ^δ,ε, u^δ,ε), where B(t) is a nonnegative bounded function for any finite time t. This work, in the special case γ≥ 3, extends the previous works, which provided the global entropy solutions for the same Cauchy problem with the restriction w(ρ^δ,ε, u^δ,ε)≤ 0 or z(ρ^δ,ε, u^δ,ε)≤ 0.
基金This study was supported by the National Natural Science Foundation of China(Grant Nos.49573192 and 49603049)
文摘The electrical conductance of 0.025 mol NaCl solution was measured at0.25-3.75 GPa and 20-370℃. As shown by the results, the conductance increases with temper-ature, and there is a liner relation between the reciprocal of temperature and the logarithm ofthe conductance but their slopes are different at different pressures. The relations between theconductance and pressure is rather complex and there are some discontinuities: in the range of2.25-3.75 GPa, the conductance increases with the pressure; in the range of 1.25-2.0 GPa, theconductance is not related to the pressure; and at a pressure of 0.75 GPa, the conductance ishigher than that at the pressures nearby. This reflects that the NaCl solution has rather differentproperties of electronic chemistry at various pressures, and probably is an important cause forthe existence of the layers with high electrical conductance and low velocity in the Earth's crustand mantle.
文摘In this paper,we consider the existence of multiple positive solutions of the following inhomepeneous semilinear elliptic equation where λ> 0.ed and ω is a bounded smooth open set in R2,h(x)∈ L 2(Ω),h(x) 0.f(t)∈ C1([0.+∝)) satisfies f(0) =f'(0)=0.fn(t) exists and fn(t)> 0.0<f(t) <Cexp(at) for some constants C,α> 0.0 <u <2 and t∈(0.+c),f(t)<0tf'(t) for someθ ∈(0,1). By looking for the local miaimum of the corresponding energy functional we tain the first minimum positive solution and by applying mountain pass lemma around the ndboum positive solution we prove the following result:
文摘The solvability of one dimensional fourth-order p-Laplace equations of the type [GRAPHICS] where, g(v) \ v \ (p-2) v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form f at zero and at infinity.
文摘We establish some results on the existence of multiple nontrivial solutions for a class of p(x)-Lap-lacian elliptic equations without assumptions that the domain is bounded. The main tools used in the proof are the variable exponent theory of generalized Lebesgue-Sobolev spaces, variational methods and a variant of the Mountain Pass Lemma.
基金This work is supported by NNSF of China (10171029).
文摘Let Ω be a smooth bounded domain in R^n. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation --△pu = ｜u｜^q-1 u ＋ λf（x） on Ω, and identify necessary and sufficient conditions on Ω and f（x） which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.
基金financial supports from the National Key Research and Development Program of China(No.2022YFB3504501)the National Natural Science Foundation of China(Nos.52274355,91962211)the Gansu Province Science and Technology Major Special Project,China(No.22ZD6GD061)。
文摘For a highly efficient recycling of a wastewater containing a high concentration of MgCl_(2),Al(Ⅲ)and P507 were scheduled to be removed in advance.In this study,the in-situ removal of Al(Ⅲ)and P507 from a high concentration MgCl_(2)solution at different pH values and Al/P molar ratios was investigated.The results showed that P507 formed organic complexes of Al_(x)(OH)_y^(Z+)-P507 at pH of 2.0-4.0.At pH of 4.0-5.0,Al(Ⅲ)precipitated and transferred into Al(OH)_(3)with a flocculent amorphous morphology.Active sites on the Al(OH)_(3)surface enhanced the removal efficiency of P507.At pH of 6.0-6.5,Al(Ⅲ)and Mg(Ⅱ)formed layered crystalline Al(OH)_(3)and MgAl_(2)(OH)_(8with)small pore channels and fewer active sites,resulting in a reduced removal efficiency of P507.When the Al/P molar ratio exceeded 13 and the pH was between 4.0 and 5.0,the removal rates of both Al(Ⅲ)and P507 were higher than98%,while the concentration loss of Mg(Ⅱ)was only 0.2%-0.9%.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
