Existence and uniqueness of periodic solutions for a p-Laplacian Duffing equation with a deviating argument

2009 ◽  
Vol 70 (10) ◽  
pp. 3567-3574 ◽  
Author(s):  
Fabao Gao ◽  
Shiping Lu ◽  
Wei Zhang
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Duffing 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.

scholarly journals Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Zaihong Wang ◽  
Jin Li ◽  
Tiantian Ma
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Duffing Equation ◽  
Deviating Argument ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions ◽  
The Given

We study the existence of periodic solutions of the second-order differential equationx′′+ax+-bx-+g(x(t-τ))=p(t), wherea,bare two constants satisfying1/a+1/b=2/n,n∈N,τis a constant satisfying0≤τ<2π,g,p:R→Rare continuous, andpis2π-periodic. When the limitslimx→±∞g(x)=g(±∞)exist and are finite, we give some sufficient conditions for the existence of2π-periodic solutions of the given equation.

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