Existence and uniqueness of periodic solutions for a kind of Liénard type -Laplacian equation

2008 ◽  
Vol 69 (2) ◽  
pp. 724-729 ◽  
Author(s):  
Bingwen Liu
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Laplacian Equation

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 for Duffing Typep-Laplacian Equation with Multiple Constant Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Hong Zhang ◽  
Junxia Meng
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Laplacian Equation ◽  
Inequality Techniques

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing typep-Laplacian equation with multiple constant delays of the form(φp(x′(t)))′+Cx′(t)+g0(t,x(t))+∑k=1ngk(t,x(t-τk))=e(t).Moreover, an example is provided to illustrate the effectiveness of the results in this paper.

scholarly journals Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1768
Author(s):  
Bin-Sheng Wang ◽  
Gang-Ling Hou ◽  
Bin Ge
Keyword(s):  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
Uniqueness Of Solutions ◽  
Laplacian Equation ◽  
Uniqueness Of The Solution ◽  
Gradient Based ◽  
Surjectivity Result ◽  
Quasilinear Elliptic

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.

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