By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l + u^p1v^q1 and vt = △v ^m + u^p2 v^q2 with homogeneous Dirichlet boundary conditions....This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l + u^p1v^q1 and vt = △v ^m + u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - (l -p1)(m- q2), the initial data, and the domain Ω.展开更多
According to the variational analysis and the potential well argument, we get the optimal conditions of global existence and blow-up for a type of nonlinear parabolic equations. Furthermore, we give its application in...According to the variational analysis and the potential well argument, we get the optimal conditions of global existence and blow-up for a type of nonlinear parabolic equations. Furthermore, we give its application in the instability of the steady states.展开更多
This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the react...This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.展开更多
The asymptotic theory of initial value problems for semilinear wave equations in two space dimensions was dealt with.The well_posedness and vaildity of formal approximations on a long time scale were discussed in the ...The asymptotic theory of initial value problems for semilinear wave equations in two space dimensions was dealt with.The well_posedness and vaildity of formal approximations on a long time scale were discussed in the twice continuous classical space. These results describe the behavior of long time existence for the validity of formal approximations. And an application of the asymptotic theory is given to analyze a special wave equation in two space dimensions.展开更多
The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely met...The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.展开更多
This article studies the inhomogeneous Moisil-Theodorsco system in the space R3, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hil...This article studies the inhomogeneous Moisil-Theodorsco system in the space R3, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R3, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved.展开更多
A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for q...A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.展开更多
By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems...By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.展开更多
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constru...Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.展开更多
Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinea...Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.展开更多
A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several exist...A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.展开更多
A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several exist...A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.展开更多
A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for...A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.展开更多
Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbau...Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.展开更多
The Cauchy problem for the semilinear wave equation has been studied and results show that the problem is locally well-posed in Hs ( Rn ) for s > max [ 0, n/2 - 1]. We extend the results by Lindblad in R3 to R2 and...The Cauchy problem for the semilinear wave equation has been studied and results show that the problem is locally well-posed in Hs ( Rn ) for s > max [ 0, n/2 - 1]. We extend the results by Lindblad in R3 to R2 and R1. The methods used in this paper are different from those of Lindblad and also the methods are more simple.展开更多
Strict feasibility is proved to be an equivalent characterization of (dual) variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This gen...Strict feasibility is proved to be an equivalent characterization of (dual) variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinitedimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.展开更多
We study the blow-up solutions for the Davey-Stewartson system(D-S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D-S system. Then, we prove the existence of ...We study the blow-up solutions for the Davey-Stewartson system(D-S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D-S system. Then, we prove the existence of minimal mass blow-up solutions. Finally, by using the characteristic of minimal mass blow-up solutions, we obtain the limiting profile and a precisely mass concentration of L2 blow-up solutions for the D-S system.展开更多
Let W be a wedge in a real Banach space X, Ω1 and Ω2 be bounded open subsets in X such that θ ∈Ω1, (?)1(?)Ω2. Our main results are as follows: Theorem 1. Let T :W ∩ (?)2 → W be a bounded P1-compact mappi...Let W be a wedge in a real Banach space X, Ω1 and Ω2 be bounded open subsets in X such that θ ∈Ω1, (?)1(?)Ω2. Our main results are as follows: Theorem 1. Let T :W ∩ (?)2 → W be a bounded P1-compact mapping. If one of the following conditions holds:展开更多
Let X be a real Banach space, F(?)X a wedge, and Ω, D two bounded open sets, 0∈Ω, (?)D. (?)_F(D_F) and (?)_F denote the boundary and closure of D_F=D(?)F relative to F respectively. CK(F) denotes the family of all ...Let X be a real Banach space, F(?)X a wedge, and Ω, D two bounded open sets, 0∈Ω, (?)D. (?)_F(D_F) and (?)_F denote the boundary and closure of D_F=D(?)F relative to F respectively. CK(F) denotes the family of all nonempty compact convex subsets of F. M=sup{||x|||x∈(?)_F(Ω_F)}+sup{||y|||y∈A_x, x∈(?)_F(Ω_F)} and M’=sup {||x|||x∈(?)_F(D_F)}+sup{||y|||y∈A_x, x∈(?)_F(D_F)}.展开更多
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金This work is supported in part by NNSF of China (10571126)in part by Program for New Century Excellent Talents in University.
文摘This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l + u^p1v^q1 and vt = △v ^m + u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - (l -p1)(m- q2), the initial data, and the domain Ω.
基金supported by National Natural Science Foundation of China(11126336 and 11201324)New Teachers’Fund for Doctor Stations,Ministry of Education(20115134120001)+1 种基金Fok Ying Tuny Education Foundation(141114)Youth Fund of Sichuan Province(2013JQ0027)
文摘According to the variational analysis and the potential well argument, we get the optimal conditions of global existence and blow-up for a type of nonlinear parabolic equations. Furthermore, we give its application in the instability of the steady states.
基金supported in part by NSF of China(11001189),supported by NSF of China(11371384)supported in part by NSF of Chongqing(cstc2013jcyjA0940)in part by NSF of Fuling(FLKJ,2013ABA2036)
文摘This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.
文摘The asymptotic theory of initial value problems for semilinear wave equations in two space dimensions was dealt with.The well_posedness and vaildity of formal approximations on a long time scale were discussed in the twice continuous classical space. These results describe the behavior of long time existence for the validity of formal approximations. And an application of the asymptotic theory is given to analyze a special wave equation in two space dimensions.
文摘The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-K-KM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.
基金Supported partially by the Key Project Foundation of the Education Department of Sichuan Province
文摘This article studies the inhomogeneous Moisil-Theodorsco system in the space R3, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R3, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved.
文摘A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.
基金This project is supported by the NNSF of China (19871059) and the Natural Science Foundation of Sichuan Education Department (2003A081).
文摘By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.
文摘Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.
基金Supported by youth foundation of Sichuan province (1999-09)
文摘Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.
文摘A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.
文摘A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.
文摘A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.
基金This project partially supported by National Natural Science Foundation of ChinaThis work was partially supported by NSERC of Canada under grant A-8096
文摘Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.
文摘The Cauchy problem for the semilinear wave equation has been studied and results show that the problem is locally well-posed in Hs ( Rn ) for s > max [ 0, n/2 - 1]. We extend the results by Lindblad in R3 to R2 and R1. The methods used in this paper are different from those of Lindblad and also the methods are more simple.
基金NSFC(Grant A0324638)Sichuan Youth Science and Technology Foundation(06ZQ026-013)SZD0406 from Sichuan Province
文摘Strict feasibility is proved to be an equivalent characterization of (dual) variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinitedimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.
基金Supported by National Natural Science Foundation of China(Grant No.11371267)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20125134120001)
文摘We study the blow-up solutions for the Davey-Stewartson system(D-S system, for short)in L2x(R2). First, we give the nonlinear profile decomposition of solutions for the D-S system. Then, we prove the existence of minimal mass blow-up solutions. Finally, by using the characteristic of minimal mass blow-up solutions, we obtain the limiting profile and a precisely mass concentration of L2 blow-up solutions for the D-S system.
文摘Let W be a wedge in a real Banach space X, Ω1 and Ω2 be bounded open subsets in X such that θ ∈Ω1, (?)1(?)Ω2. Our main results are as follows: Theorem 1. Let T :W ∩ (?)2 → W be a bounded P1-compact mapping. If one of the following conditions holds:
文摘Let X be a real Banach space, F(?)X a wedge, and Ω, D two bounded open sets, 0∈Ω, (?)D. (?)_F(D_F) and (?)_F denote the boundary and closure of D_F=D(?)F relative to F respectively. CK(F) denotes the family of all nonempty compact convex subsets of F. M=sup{||x|||x∈(?)_F(Ω_F)}+sup{||y|||y∈A_x, x∈(?)_F(Ω_F)} and M’=sup {||x|||x∈(?)_F(D_F)}+sup{||y|||y∈A_x, x∈(?)_F(D_F)}.