Variational Approaches to Characterize Weak Solutions for Some Problems of Mathematical Physics Equations

Abstract

This paper is aimed at providing three versions to solve and characterize weak solutions for Dirichlet problems involving the $p$-Laplacian and the $p$-pseudo-Laplacian. In this way generalized versions for some results which use Ekeland variational principle, critical points for nondifferentiable functionals, and Ghoussoub-Maurey linear principle have been proposed. Three sequences of generalized statements have been developed starting from the most abstract assertions until their applications in characterizing weak solutions for some mathematical physics problems involving the abovementioned operators.