Multiplicity of solutions for a nonhomogeneous quasilinear elliptic problem with critical growth

2017/03/24 by Marcos L. M. Carvalho, J.V. Gonçalves, Carvalho, M. L. M. +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.08592

openalex publication_date 2017/03/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

It is established some existence and multiplicity of solution results for a quasilinear elliptic problem driven by Φ-Laplacian operator. One of these solutions is built as a ground state solution. In order to prove our main results we apply the Nehari method combined with the concentration compactness theorem in an Orlicz-Sobolev framework. One of the difficulties in dealing with this kind of operator is the lost of homogeneity properties.

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