Competing anisotropic and Finsler ( p , q ) $(p,q)$ -Laplacian problems

Abstract

Abstract The aim of this paper is to prove the existence of generalized variational solutions for nonlinear Dirichlet problems driven by anisotropic and Finsler Laplacian competing operators. The main difficulty consists in the lack of ellipticity and monotonicity in the principal part of the equations. This difficulty is overcome by developing a Galerkin-type procedure.

Keywords

• Generalized variational solution
• Anisotropic p-Laplacian
• Finsler Laplacian
• Galerkin scheme