Abstract
In this work, we investigate the following p-Laplacian Lienard equation: ('p(x 0 (t))) 0 + f(x(t))x 0 (t) + g(x(t)) = e(t). Under some assumption, a necessary and sufficient condition f or the existence and uniqueness of periodic solutions of this equation is given by using Manasevich-Mawhin continuation theorem. Our results improve and extend some known results.
Highlights
IntroductionWe investigate the existence and uniqueness of periodic solutions of the following p-Laplacian
In this paper, we investigate the existence and uniqueness of periodic solutions of the following p-LaplacianLienard equation (φp(x′(t)))′ + f (x(t))x′(t) + g(x(t)) = e(t), (1.1)where p > 1, φp : R → R is given by φp(s) = |s|p−2s for s = 0, φp(0) = 0, f, g, e ∈ C(R, R) and e is T -periodic with T > 0
Where p > 1, φp : R → R is given by φp(s) = |s|p−2s for s = 0, φp(0) = 0, f, g, e ∈ C(R, R) and e is T -periodic with T > 0
Summary
We investigate the existence and uniqueness of periodic solutions of the following p-Laplacian. Generalized Lienard equations appear in a number of physical models, and the problem concerning the periodic solutions for these equations has been studied extensively by lots of authors; see for example [1,2,3,4,5,6,7,8,9,10,11,12] and the references therein. In many nonlinear problems arising in practical dynamical systems, physical reasoning alone is not sufficient or fully convincing. In these cases questions of existence and uniqueness are of importance in understanding the full range of solution behaviour possible, and represent a genuine mathematical challenge. Our results improve and extend some results in [6] (see Remark 2 and Examples 1 and 2)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
