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.

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.

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.

scholarly journals Existence of Periodic Solutions for a Class of Asymptoticallyp-Linear Discrete Systems Involvingp-Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Kai Chen ◽  
Qiongfen Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Mountain Pass Theorem ◽  
Discrete Systems ◽  
Point Theory ◽  
Existence Results ◽  
Existence Of Periodic Solutions ◽  
Linear Discrete Systems

By applying Mountain Pass Theorem in critical point theory, two existence results are obtained for the following asymptoticallyp-linearp-Laplacian discrete systemΔ(|Δu(t−1)|p−2Δu(t−1))+∇[−K(t,u(t))+W(t,u(t))]=0. The results obtained generalize some known works.

scholarly journals Periodic Solutions with Prescribed Minimal Period for 2 n th-Order Nonlinear Discrete Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Haiping Shi ◽  
Peifang Luo ◽  
Zan Huang
Keyword(s):  
Periodic Solutions ◽  
Discrete System ◽  
Discrete Systems ◽  
Point Theory ◽  
Minimal Period ◽  
Main Approach ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Nonlinear Discrete System ◽  
Nonlinear Discrete Systems

In this paper, by using the critical point theory, some new results of the existence of at least two nontrivial periodic solutions with prescribed minimal period to a class of 2 n th-order nonlinear discrete system are obtained. The main approach used in our paper is variational technique and the linking theorem. The problem is to solve the existence of periodic solutions with prescribed minimal period of 2 n th-order discrete systems.

Impulsive differential inclusions via variational method

2017 ◽  
Vol 24 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Mouffak Benchohra ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Differential Inclusion ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Impulsive Differential Inclusions

AbstractIn this paper, we establish several results about the existence of second-order impulsive differential inclusion with periodic conditions. By using critical point theory, several new existence results are obtained. We also provide an example in order to illustrate the main abstract results of this paper.

scholarly journals Periodic Solutions of Second-Order Differential Inclusions Systems with -Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Liang Zhang ◽  
Peng Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Nonsmooth Critical Point Theory ◽  
Nonsmooth Critical Point ◽  
Existence Of Periodic Solutions

The existence of periodic solutions for nonautonomous second-order differential inclusion systems with -Laplacian is considered. We get some existence results of periodic solutions for system, a.e. , , by using nonsmooth critical point theory. Our results generalize and improve some theorems in the literature.

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