A New Approach to the Existence of Quasiperiodic Solutions for Second-Order Asymmetric p-Laplacian Differential Equations
Joint Authors
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-19
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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/psinπ/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.
American Psychological Association (APA)
Wang, Xiaoming& Wang, Lixia. 2018. A New Approach to the Existence of Quasiperiodic Solutions for Second-Order Asymmetric p-Laplacian Differential Equations. Journal of Function Spaces،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1186618
Modern Language Association (MLA)
Wang, Xiaoming& Wang, Lixia. A New Approach to the Existence of Quasiperiodic Solutions for Second-Order Asymmetric p-Laplacian Differential Equations. Journal of Function Spaces No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1186618
American Medical Association (AMA)
Wang, Xiaoming& Wang, Lixia. A New Approach to the Existence of Quasiperiodic Solutions for Second-Order Asymmetric p-Laplacian Differential Equations. Journal of Function Spaces. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1186618
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186618