scholarly journals EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A KIND OF RAYLEIGH EQUATION WITH A DEVIATING ARGUMENT

2007 ◽  
Vol 44 (3) ◽  
pp. 673-682
Author(s):  
Qiyuan Zhou ◽  
Bing Xiao ◽  
Yuehua Yu ◽  
Bingwen Liu ◽  
Lihong Huang
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Rayleigh Equation ◽  
Deviating Argument

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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