Existence results for Schrödinger p(⋅)-Laplace equations involving critical growth in RN. (May 2019)

• Record Type: Journal Article
• Authors: Ho, Ky; Kim, Yun-Ho; Sim, Inbo
• Is Part Of: Nonlinear analysis. Volume 182(2019)
• Page Start: 20
• Page End: 44
• Publication Date: 2019-05
• Subjects: 35J62 -- 35B33 -- 35J20 -- 35J25 -- 35J70 -- 46E35; p(⋅)-Laplacian -- Weighted variable exponent Sobolev spaces -- Concentration-compactness principle; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.12.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish some existence results for Schrödinger p ( ⋅ ) -Laplace equations in R N with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space R N . The proofs are mainly based on concentration-compactness principles in a suitable weighted variable exponent Sobolev space and its imbeddings.