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Author Wang, Xiaoming ♦ Wang, Lixia
Editor Wang, Liguang
Source Hindawi
Content type Text
Publisher Hindawi
File Format PDF
Copyright Year ©2018
Language English
Abstract For p≥2 and ϕp(s):=sp-2s, we propose a new estimate approach to study the existence of Aubry-Mather sets and quasiperiodic solutions for the second-order asymmetric p-Laplacian differential equations ϕpx′′+λϕp(x+)-μϕp(x-)=ψ(t,x), where λ and μ are two positive constants satisfying λ-1/p+μ-1/p=2/ω with ω∈R+, ψ(t,x)∈C0,1(Sp×R) is a continuous function, 2πp-periodic in the first argument and continuously differentiable in the second one, x±=max⁡{±x,0}, πp=2π(p-1)1/p/psin⁡π/p, and Sp=R/2πpZ. Using the Aubry-Mather theorem given by Pei, we obtain the existence of Aubry-Mather sets and quasiperiodic solutions under some reasonable conditions. Particularly, the advantage of our approach is that it not only gives a simpler estimation procedure, but also weakens the smoothness assumption on the function ψ(t,x) in the existing literature.
ISSN 23148896
Learning Resource Type Article
Publisher Date 2018-06-19
Rights License This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
e-ISSN 23148888
Journal Journal of Function Spaces
Volume Number 2018
Page Count 9


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