In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtain...In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.展开更多
In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the p...We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the problem has at least one nontrivial weak solution.展开更多
In this paper, we consider the existence for periodic solutions of nonau- tonomons second-order differential systems with （q,p）-Laplacian by using the least action principle and the minimax methods.
In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity the...In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.展开更多
Two results about the multiplicity of nontrivial periodic bouncing solutions for sublinear damped vibration systems-x=g(t)x+f(t,x) are obtained via the Generalized Nonsmooth Saddle Point Theorem and a technique establ...Two results about the multiplicity of nontrivial periodic bouncing solutions for sublinear damped vibration systems-x=g(t)x+f(t,x) are obtained via the Generalized Nonsmooth Saddle Point Theorem and a technique established by Wu Xian and Wang Shaomin.Both of them imply the condition "f≥0" required in some previous papers can be weakened,furthermore,one of them also implies the condition about ■F(t,x)/■t required in some previous papers,such as "|■F(t,x)/■t|=σ_(0)F(t,x)" and "|■F(t,x)/■t|≤C(1+F(t,x))", is unnecessary,where F(t,x):=∫_(0)~xf(t,x)ds,and σ_(0),C are positive constants.展开更多
The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.
The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need ...The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need additional conditions to ensure the existence of periodic bouncing solutions.展开更多
In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is var...In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic and subharmonic solutions of second order forward and backward difference equations.展开更多
This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -△u=λu- a...This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -△u=λu- a（x）｜u｜q-1u-f（x,u）,with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.展开更多
In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some ne...In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.展开更多
文摘In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.
基金Foundation item： Supported by the Sichuan Educational Comittee Science Foundation for Youths（08ZB002） Supported by the National Secience Foundation of Yibin University（2008Z02）
文摘In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
文摘We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the problem has at least one nontrivial weak solution.
基金The NSF (10871059 and 10671028) of Chinathe Fundamental Research Founds (B09020181) for the Central Universities
文摘In this paper, we consider the existence for periodic solutions of nonau- tonomons second-order differential systems with （q,p）-Laplacian by using the least action principle and the minimax methods.
基金Supported by the Youth Foundation of Shangqiu Institute of Technology(No.2018XKQ01)
文摘In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.
基金Supported by the National Natural Science Foundation of China (Grant No. 12171355)Elite Scholar Program in Tianjin University,P. R. China。
文摘Two results about the multiplicity of nontrivial periodic bouncing solutions for sublinear damped vibration systems-x=g(t)x+f(t,x) are obtained via the Generalized Nonsmooth Saddle Point Theorem and a technique established by Wu Xian and Wang Shaomin.Both of them imply the condition "f≥0" required in some previous papers can be weakened,furthermore,one of them also implies the condition about ■F(t,x)/■t required in some previous papers,such as "|■F(t,x)/■t|=σ_(0)F(t,x)" and "|■F(t,x)/■t|≤C(1+F(t,x))", is unnecessary,where F(t,x):=∫_(0)~xf(t,x)ds,and σ_(0),C are positive constants.
文摘The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.
基金Supported by National Natural Science Foundation of China(Grant Nos.11501308,11271277 and 11571249)Jiangsu Government Scholarship for Overseas Studies
文摘The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need additional conditions to ensure the existence of periodic bouncing solutions.
文摘In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic and subharmonic solutions of second order forward and backward difference equations.
文摘This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -△u=λu- a（x）｜u｜q-1u-f（x,u）,with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.
基金supported by Science and Technology Plan Foundation of Guangzhou(No.2006J1-C0341)
文摘In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.
