On supercritical problems involving the Laplace operator. Issue 1 (February 2021)

• Record Type: Journal Article
• Authors: Clemente, Rodrigo; Marcos do Ó, João; Ubilla, Pedro
• Is Part Of: Proceedings. Volume 151:Issue 1(2021)
• Page Start: 187
• Page End: 201
• Publication Date: 2021-02
• Subjects: Critical Sobolev exponent, -- Supercritical elliptic problems, -- Radial solutions; 35J20, -- 35J25, -- 35J50; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2020.9
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract: We discuss the existence, nonexistence and multiplicity of solutions for a class of elliptic equations in the unit ball with zero Dirichlet boundary conditions involving nonlinearities with supercritical growth. By using Pohozaev type identity we prove a nonexistence result for a class of supercritical problems with variable exponent which allow us to complement the analysis developed in (Calc. Var. (2016) 55:83). Moreover, we establish existence results of positive solutions for semilinear elliptic equations involving nonlinearities which are subcritical at infinity just in a part of the domain, and can be supercritical in a suitable sense.