Multiple weak solutions for a kind of time-dependent equation involving singularity

TL;DR

This paper proves the existence of at least three weak solutions for a nonlinear time-dependent equation with a singular source term at the origin, using variational methods and critical point theory.

Contribution

It introduces a novel approach to handle singularities in time-dependent equations and establishes multiple weak solutions where previously only existence was known.

Findings

At least three weak solutions exist for the considered equation.

The methods effectively handle singular source functions at the origin.

Variational techniques are successfully applied to this class of problems.

Abstract

The existence of at least three weak solutions for a kind of nonlinear time-dependent equation is studied. In fact, we consider the case that the source function has singularity at origin. To this aim, the variational methods and the well-known critical points theorem are main tools.