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

2023/09/09 by Lakhdari, Abderrahmane, Rhouma, Nedra Belhaj
#35A21 #35J99 #35P30 #35R11 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2309.04804

Abstract

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 φ-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 Δ₂-condition. Our main results are obtained through technical proofsthat combine a Lagrange multipliers type approach with the Ljusternik-Schnirelmann argument.

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