Existence and uniqueness of weak solutions to singular anisotropic elliptic problems

TL;DR

This paper investigates the existence and uniqueness of weak solutions for a class of singular anisotropic elliptic problems, establishing conditions under which solutions exist and are unique.

Contribution

It provides new criteria for existence and uniqueness of weak solutions in singular anisotropic elliptic problems, extending previous theoretical frameworks.

Findings

Proved uniqueness of weak solutions.

Established necessary and sufficient conditions for existence.

Extended classical results to anisotropic singular problems.

Abstract

In this paper we consider a quasilinear singular anisotropic elliptic problem with a p-sublinear perturbation. We prove uniqueness of weak solutions and we provide necessary and sufficient conditions for the existence of weak solutions in the same spirit of the celebrated paper by Lazer and McKenna.