Existence of weak solutions to degenerate Leray–Lions operators in weighted quasilinear elliptic equations with variable exponents, indefinite nonlinearity, and Hardy-type term

Abstract

This paper investigates multiplicity results of weak solutions to a degenerate weighted elliptic problem involving Leray–Lions operators with indefinite nonlinearity and variable exponents. Using critical point theory, we establish the existence of at least one, respectively three weak solutions under suitable assumptions. The results extend to a wide range of nonlinear problems in mathematical physics, addressing the complications arising from degeneracy, Hardy-type singularities, and indefinite source terms.