On a class of weighted anisotropic $p$-Laplace equation with singular nonlinearity

TL;DR

This paper studies a class of weighted anisotropic p-Laplace equations with singular nonlinearities, establishing conditions for the existence and multiplicity of weak solutions depending on the behavior of the weight function.

Contribution

It provides new sufficient conditions on the weight function that guarantee existence and multiplicity of solutions in singular anisotropic p-Laplace equations.

Findings

Existence of at least one weak solution in the purely singular case.

Existence of at least two weak solutions in the perturbed singular case.

Conditions on the weight function near the origin are crucial for solution existence.

Abstract

We consider a class of singular weighted anisotropic $p$-Laplace equations. We provide sufficient condition on the weight function that may vanish or blow up near the origin to ensure the existence of at least one weak solution in the purely singular case and at least two different weak solutions in the purturbed singular case.