This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of...This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.展开更多
In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the f...In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.展开更多
Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjectur...Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.展开更多
In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a ge...In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of 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
Based on the Leggett-Williams fixed point theorem for a Banach space, we establish the existence of three positive periodic solutions for a class of delay difference equations.
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
Using the Krasnoselskii＇s fixed point theorem, the existence of positive periodic solutions to a class of nonlinear functional difference equations is studied in this paper. Some sufficient conditions for the existen...Using the Krasnoselskii＇s fixed point theorem, the existence of positive periodic solutions to a class of nonlinear functional difference equations is studied in this paper. Some sufficient conditions for the existence of positive periodic solutions are presented.展开更多
By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_...By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.展开更多
In this paper, a 2 nth-order nonlinear difference equation is considered.Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic solutions.Resu...In this paper, a 2 nth-order nonlinear difference equation is considered.Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic solutions.Results obtained complement or improve the existing ones.展开更多
A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
基金Supported by the Natural Science Foundation of Hunan Province（12JJ6006） Supported by the Science Foundation of Department of Science and Technology of Hunan Province（2012FJ3107）
文摘This paper is concerned with the nonlinear neutral functional difference equations△x(n) =-a(n)x(n) +h(n)f(n,x(n-T(n)),△x(n-δ(n))),where a,h and f are nonnegative sequences.Sufficient conditions for the existence of at least three positive T-periodic solutions are established by using a fixed point theorem due to Avery and Peterson.
基金Project(10471153) supported by the National Natural Science Foundation of China project supported by the Natural Science Foundation of Central South University
文摘In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.
文摘Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.
基金Supported by Program for Changjiang Scholars and Innovative Research Team in University (Grant No.IRT1226)National Natural Science Foundation of China (Grant Nos. 11171078 and 11031002)the Specialized Fund for the Doctoral Program of Higher Education of China (Grant No. 20114410110002)
文摘In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of 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.
基金Project partially supported by Natural Science Foundation of Shanxi Province and Yanbei Normal University and by High Science and Technology Foundation of Shanxi Province and by Science and Technology Bureau of Datong City.
文摘Based on the Leggett-Williams fixed point theorem for a Banach space, we establish the existence of three positive periodic solutions for a class of delay difference equations.
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.
基金Project supported by National Natural Sciences Foundation of China (10572021).
文摘Using the Krasnoselskii＇s fixed point theorem, the existence of positive periodic solutions to a class of nonlinear functional difference equations is studied in this paper. Some sufficient conditions for the existence of positive periodic solutions are presented.
基金This work was supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE of Chinaby the Trans-Century Training Programme Foundation for the Talents of the State Education Commissionby the National Natural Science Foundation of China(Grant No.19831030).
文摘By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.
基金supported by Specialized Fund for the Doctoral Program of Higher Eduction (Grant No.20071078001)National Natural Science Foundation of China (Grant No.10625104)Natural Science and Engineering Reserach Council of Canada (NSERC)
文摘In this paper, a 2 nth-order nonlinear difference equation is considered.Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic solutions.Results obtained complement or improve the existing ones.
基金Supported by the NNSFC(10071022),Mathematical Tianyuan Foundation of China(Ty10026002-01-05-03)Shanghai Priority Academic Discipline.
文摘A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
