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.

scholarly journals Existence of periodic solutions with prescribed minimal period of a 2nth-order discrete system

2019 ◽  
Vol 17 (1) ◽  
pp. 1392-1399
Author(s):  
Xia Liu ◽  
Tao Zhou ◽  
Haiping Shi
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Minimal Period ◽  
Existence Of Periodic Solutions ◽  
First Time

Abstract In this paper, we concern with a 2nth-order discrete system. Using the critical point theory, we establish various sets of sufficient conditions for the existence of periodic solutions with prescribed minimal period. To the best of our knowledge, this is the first time to discuss the periodic solutions with prescribed minimal period for a 2nth-order discrete system.

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 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.

Periodic solutions of higher-dimensional discrete systems

2004 ◽  
Vol 134 (5) ◽  
pp. 1013-1022 ◽  
Author(s):  
Zhan Zhou ◽  
Jianshe Yu ◽  
Zhiming Guo
Keyword(s):  
Positive Integer ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Discrete Systems ◽  
Point Theory ◽  
Second Order ◽  
Higher Dimensional ◽  
Image Position

Consider the second-order discrete system where f ∈ C (R × Rm, Rm), f(t + M, Z) = f(t, Z) for any (t, Z) ∈ R × Rm and M is a positive integer. By making use of critical-point theory, the existence of M-periodic solutions of (*) is obtained.

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.

scholarly journals Periodic Solutions and Nontrivial Periodic Solutions for a Class of Rayleigh-Type Equation with Two Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Meiqiang Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type Equation ◽  
Index Theorem ◽  
Rayleigh Equation ◽  
Deviating Arguments ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions

The Rayleigh equation with two deviating argumentsx′′(t)+f(x'(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=e(t)is studied. By using Leray-Schauder index theorem and Leray-Schauder fixed point theorem, we obtain some new results on the existence of periodic solutions, especially for the existence of nontrivial periodic solutions to this equation. The results are illustrated with two examples, which cannot be handled using the existing results.

scholarly journals ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF NONLINEAR DIFFERENTIAL SYSTEMS

1993 ◽  
Vol 24 (2) ◽  
pp. 173-188
Author(s):  
LIHONG HUANG ◽  
JIANSHE YU
Keyword(s):  
Periodic Solutions ◽  
Special Form ◽  
Differential Systems ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Nonlinear Differential Systems

In this paper three theorems on the existence of nontrivial periodic solutions of the system \[ dx/dt =e(y)\]\[dy/dt =-e(y)f(x)- g(x)\] are proved, which not only generalize some known results on the existence of periodic solutions of Lienard's system (i.e. the special form for $e(y) = y$), but also relax or eliminate some traditional assumptions.

scholarly journals Periodic Solutions for a Class of Singular Hamiltonian Systems on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiaofang Meng ◽  
Yongkun Li
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Time Scales ◽  
Critical Point Theory ◽  
Point Theory ◽  
Singular Hamiltonian Systems ◽  
Existence Of Periodic Solutions

We are concerned with a class of singular Hamiltonian systems on time scales. Some results on the existence of periodic solutions are obtained for the system under consideration by means of the variational methods and the critical point theory.

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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