scholarly journals Existence of periodic solutions for a fourth-order p-Laplacian equation with a deviating argument

2009 ◽  
Vol 230 (2) ◽  
pp. 513-520 ◽  
Author(s):  
Shiping Lu ◽  
Shan Jin
Keyword(s):  
Periodic Solutions ◽  
Fourth Order ◽  
Deviating Argument ◽  
Laplacian Equation ◽  
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 Study Of Asymptotically Almost Periodic Solutions of a Class of Impulsive Population Models

2018 ◽  
Vol 36 (3) ◽  
pp. 597-601
Author(s):  
Li Wang
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Population Models ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Laplacian Equation ◽  
Existence Of Periodic Solutions ◽  
Functional Differential ◽  
Solutions Of Equations ◽  
Asymptotically Almost Periodic

Based on the Mawhin continuous theorem, the existence of strictly positive asymptotically almost periodic solutions of a class of impulsive population models is studied. The conclusion generalizes the conclusion of the existing literatures. Since the Mawhin continuous theorem is only used to prove the existence of periodic solutions or almost periodic solutions of equations (for example:impulsive differential equation, functional differential equation, integral equation, Lienard equation, P-Laplacian equation), the main result is innovative.

scholarly journals Some Results for Periodic Solutions of a Kind of Liénard Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Yong Wang ◽  
Xiangyi Yi
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Continuation Theorem ◽  
Deviating Argument ◽  
Laplacian Equation ◽  
Analysis Techniques ◽  
Weaker Conditions ◽  
New Criteria ◽  
Mawhin Continuation Theorem ◽  
Theoretical Results

We investigate the following Liénard-typep-Laplacian equation with a deviating argument(φp(x′t))′+f(xt)x′t+βtgxt-τt=e(t). Some new criteria for guaranteeing the existence and uniqueness of periodic solutions of this equation are given by using the Manásevich-Mawhin continuation theorem and some analysis techniques. Our results hold under weaker conditions than some known results from the literature and are more effective. In the last section, an illustrative example is provided to demonstrate the applications of the theoretical results.

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