Nonlinear fractional magnetic Schrödinger equation: existence and multiplicity

2017/09/24 by Ambrosio, Vincenzo, d'Avenia, Pietro
#35A15 #35R11 #35S05 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.08207

Abstract

In this paper we focus our attention on the following nonlinear fractional Schrödinger equation with magnetic field ε^2s(-Δ)_A/ε^su+V(x)u=f(|u|²)u in ℝ^N, where ε>0 is a parameter, s∈ (0, 1), N≥ 3, (-Δ)^s_A is the fractional magnetic Laplacian, V:ℝ^N→ ℝ and A:ℝ^N→ ℝ^N are continuous potentials and f:ℝ^N→ ℝ is a subcritical nonlinearity. By applying variational methods and Ljusternick-Schnirelmann theory, we prove existence and multiplicity of solutions for ε small.

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