Multiplicity and concentration results for a magnetic Schrödinger equation with exponential critical growth in ℝ²

2019/06/26 by d'Avenia, Pietro, Ji, Chao
#35B33 #35J20 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.10937

Abstract

In this paper we study the following nonlinear Schrödinger equation with magnetic field ((ε)/(i)∇-A(x))²u+V(x)u=f(| u|²)u, x∈ℝ², where ε>0 is a parameter, V:ℝ²→ ℝ and A: ℝ²→ ℝ² are continuous potentials and f:ℝ→ ℝ has exponential critical growth. Under a local assumption on the potential V, by variational methods, penalization technique, and Ljusternick-Schnirelmann theory, we prove multiplicity and concentration of solutions for ε small.

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