An existence result for anisotropic quasilinear problems. (June 2022)

• Record Type: Journal Article
• Authors: Agudelo, Oscar; Drábek, Pavel
• Is Part Of: Nonlinear analysis. Volume 65(2022)
• Publication Date: 2022-06
• Subjects: p-Laplacian -- Quasilinear eigenvalue problems -- Subsolution and supersolution -- Weighted Sobolev spaces -- Kato estimates -- (p−1)-sublinearity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103345
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted p -Laplacian operator with a coefficient that is locally bounded inside the domain and satisfying certain additional integrability assumptions. Our main result applies for boundary value problems involving continuous non-linearities having no growth restriction, but provided the existence of a sub and a supersolution is guaranteed. As an application, we present an existence result for a boundary value problem with a non-linearity f ( u ) satisfying f ( 0 ) ≤ 0 and having ( p − 1 ) -sublinear growth at infinity.