Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods
Joint Authors
Li, Shengjun
Luo, Huxiao
Tang, XianHua
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-11-21
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We study the existence of nontrivial solution of the following equation without compactness: (-Δ)pαu+up-2u=f(x,u), x∈RN, where N,p≥2, α∈(0,1), (-Δ)pα is the fractional p-Laplacian, and the subcritical p-superlinear term f∈C(RN×R) is 1-periodic in xi for i=1,2,…,N.
Our main difficulty is that the weak limit of (PS) sequence is not always the weak solution of fractional p-Laplacian type equation.
To overcome this difficulty, by adding coercive potential term and using mountain pass theorem, we get the weak solution uλ of perturbation equations.
And we prove that uλ→u as λ→0.
Finally, by using vanishing lemma and periodic condition, we get that u is a nontrivial solution of fractional p-Laplacian equation.
American Psychological Association (APA)
Luo, Huxiao& Li, Shengjun& Tang, XianHua. 2017. Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1123220
Modern Language Association (MLA)
Luo, Huxiao…[et al.]. Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods. Advances in Mathematical Physics No. 2017 (2017), pp.1-9.
https://search.emarefa.net/detail/BIM-1123220
American Medical Association (AMA)
Luo, Huxiao& Li, Shengjun& Tang, XianHua. Nontrivial Solution for the Fractional p-Laplacian Equations via Perturbation Methods. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1123220
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123220