The Fredholm alternative for the p-Laplacian in exterior domains. (September 2018)

• Record Type: Journal Article
• Authors: Drábek, Pavel; Ho, Ky; Sarkar, Abhishek
• Is Part Of: Nonlinear analysis. Volume 174(2018)
• Page Start: 17
• Page End: 53
• Publication Date: 2018-09
• Subjects: 35J92 -- 35J60 -- 35J20 -- 35P30 -- 35J62 -- 35B40; p-Laplacian -- Fredholm alternative -- The first eigenvalue -- Exterior domain -- Variational method; 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.2018.04.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the Fredholm alternative for the p -Laplacian in an exterior domain which is the complement of the closed unit ball in R N ( N ≥ 2 ). By employing techniques of Calculus of Variations we obtain the multiplicity of solutions. The striking difference between our case and the entire space case is also discussed.