Multiplicity and concentration behavior of solutions for a quasilinear problem involving N-functions via penalization method

2015/06/17 by Claudianor O. Alves, Alves, Claudianor O., Ailton R. da Silva +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1506.05331

arXiv admin note: text overlap with arXiv:1506.01669

arxiv created 2015/06/17 · openalex publication_date 2015/06/17 · arxiv updated 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study the existence, multiplicity and concentration of positive solutions for the following class of quasilinear problem: - Δ_Φu + V(εx)ϕ(\vert u\vert)u = f(u) in ℝ^N, where Φ(t) = ∫₀^{\vert t\vert}ϕ(s)sds is a N-function, Δ_Φ is the Φ-Laplacian operator, ε is a positive parameter, N≥ 2, V : ℝ^N → ℝ is a continuous function and f : ℝ → ℝ is a C¹-function.

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