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 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 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 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 Periodic Solutions for Semilinear Fourth-Order Differential Inclusions via Nonsmooth Critical Point Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bian-Xia Yang ◽  
Hong-Rui Sun
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Nonsmooth Critical Point Theory ◽  
Critical Point Theorem ◽  
Related Literature ◽  
Nonsmooth Critical Point

Three periodic solutions with prescribed wavelength for a class of semilinear fourth-order differential inclusions are obtained by using a nonsmooth version critical point theorem. Some results of previous related literature are extended.

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.

Wright's equation has no solutions of period four

1989 ◽  
Vol 113 (3-4) ◽  
pp. 281-288 ◽  
Author(s):  
Roger D. Nussbaum
Keyword(s):  
Periodic Solutions ◽  
Fourth Order ◽  
Delay Equations ◽  
Order System ◽  
Minimal Period ◽  
Differential Delay ◽  
Differential Delay Equations

SynopsisLet N:ℝ→ℝ be a locally Lipschitzian map such that (y + l)N(y)>0 for all y ≠ –1 and such that N(y)=1 + y for – 1 ≦ y ≦ 3. For any positive number α the equation y'(t) αy(t–1)N(y(t)) has, aside from the constantsolutions y(t) ≡ –1, and y(t) ≡–1 solution y(t) such that y(t + 4) = y(t) for all real t If N(y) = 1 + y for all y, one obtains Wright's equation, which isknown to have periodic solutions of minimal period p (depending on α) arbitrarily close to 4. Some results concerning nonexistence of periodic solutions of period 4 of other differential-delay equations are also proved. In all cases the method of proof consists in analysing an associated fourth-order system of ordinary differential equationsand showing that this system has no nonconstant periodic solutions.

Sign in / Sign up

Export Citation Format

Share Document