Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents

Abstract

This paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least three weak solutions under general assumptions on the weight function and the nonlinearity. This result has wide applicability, extending existing theories on quasilinear elliptic equations.

Keywords

• variational methods
• hardy inequality
• degenerate $ p(x) $-laplacian operators