On a class of critical double phase problems

Author(s)

Farkas, Csaba ; Fiscella, Alessio ; Winkert, Patrick

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 515, n. 2, p. 16-pg., 2022-11-15.

Abstract

In this paper we study a class of double phase problems involving critical growth, namely -div (|del u|(p-2)del u + mu(x)|del u|(q-2)del u) =lambda|u|(upsilon-2)u + |u|(p*-2)u in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N is a bounded Lipschitz domain, 1 < upsilon < p < q< N, q< p* and mu(center dot) is a nonnegative bounded weight function. The operator involved is the so-called double phase operator, which reduces to the p-Laplacian or the ( p, q)-Laplacian when mu = 0or inf mu > 0, respectively. Based on variational and topological tools such as truncation arguments and genus theory, we show the existence of lambda*> 0such that the problem above has infinitely many weak solutions with negative energy values for any lambda is an element of(0, lambda*). (c) 2022 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 19/23917-3 - Operator with non standard growth
• Grantee: Alessio Fiscella
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/02512-5 - Systems and partial differential equations
• Grantee: Marcelo da Silva Montenegro
• Support Opportunities: Research Projects - Thematic Grants