Multiplicity of Solutions for a problem in double weighted Orlicz-Sobolev and its spectrum

The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We also examine the presence of sequences of variational eigenvalues in two distinct scenarios, one with and one without assuming the {Δ_2}-condition. Our main results are obtained through technical proofsthat combine a Lagrange multipliers type approach with the Ljusternik-Schnirelmann argument.