scholarly journals Existence of periodic solutions of fourth-order nonlinear difference equations

2013 ◽  
Vol 108 (2) ◽  
pp. 811-825 ◽  
Author(s):  
Haiping Shi ◽  
Xia Liu ◽  
Yuanbiao Zhang ◽  
Xiaoqing Deng
Keyword(s):  
Periodic Solutions ◽  
Fourth Order ◽  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions

scholarly journals Periodic Solutions with Minimal Period for Fourth-Order Nonlinear Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xia Liu ◽  
Tao Zhou ◽  
Haiping Shi ◽  
Yuhua Long ◽  
Zongliang Wen
Keyword(s):  
Periodic Solutions ◽  
Fourth Order ◽  
Point Theory ◽  
Nonlinear Difference Equation ◽  
Linking Theorem ◽  
Variational Technique ◽  
Minimal Period ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions ◽  
New Criteria

A fourth-order nonlinear difference equation is considered. By making use of critical point theory, some new criteria are obtained for the existence of periodic solutions with minimal period. The main methods used are a variational technique and the Linking Theorem.

scholarly journals On the Periodicity of General Class of Difference Equations

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 75 ◽  
Author(s):  
Osama Moaaz ◽  
Hamida Mahjoub ◽  
Ali Muhib
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
General Class ◽  
Sufficient Conditions ◽  
Usual Method ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient

In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method.

Existence of periodic solutions with minimal period for fourth-order discrete systems via variational methods

2020 ◽  
Vol 21 (6) ◽  
pp. 635-640
Author(s):  
Lianwu Yang
Keyword(s):  
Periodic Solution ◽  
Variational Method ◽  
Fourth Order ◽  
Difference Equations ◽  
Discrete Systems ◽  
Point Theory ◽  
Existence Results ◽  
Minimal Period ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions

AbstractBy using critical point theory, some new existence results of at least one periodic solution with minimal period pM for fourth-order nonlinear difference equations are obtained. Our approach used in this paper is a variational method.

Existence of periodic solutions of fourth-order p-Laplacian difference equations

2016 ◽  
Vol 53 (1) ◽  
pp. 53-73
Author(s):  
Haiping Shi ◽  
Xia Liu ◽  
Yuanbiao Zhang
Keyword(s):  
Saddle Point ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Point Theory ◽  
Saddle Point Theorem ◽  
Variational Technique ◽  
Main Approach ◽  
Existence Of Periodic Solutions

By making use of the critical point theory, the existence of periodic solutions for fourth-order nonlinear p-Laplacian difference equations is obtained. The main approach used in our paper is a variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions of fourth-order nonlinear p-Laplacian difference equations. The results obtained successfully generalize and complement the existing one.

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