Multiple solutions for a NLS equation with critical growth and magnetic field

2013/04/17 by Claudianor O. Alves, Alves, Claudianor O., Giovany M. Figueiredo +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1304.4767

arxiv created 2013/04/17 · openalex publication_date 2013/04/17 · arxiv updated 2013/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the multiplicity of nontrivial solutions for the following class of complex problems (-i∇ - A(μx))²u= μ|u|^q-2u + |u|^2^*-2u in Ω, u ∈ H¹₀(Ω,ℂ), where Ω⊂ ℝ^N (N ≥ 4) is a bounded domain with smooth boundary. Using the Lusternik-Schnirelman theory, we relate the number of solutions with the topology of Ω.

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