Concentration phenomena for fractional magnetic NLS equations

Abstract

We study the multiplicity and concentration of complex valued solutions for a fractional magnetic Schrödinger equation involving a scalar continuous electric potential satisfying a local condition and a continuous nonlinearity with subcritical growth. The main results are obtained by applying a penalization technique, generalized Nehari manifold method and Ljusternik-Schnirelman theory. We also prove a Kato's inequality for the fractional magnetic Laplacian which we believe to be useful in the study of other fractional magnetic problems.

arXiv admin note: text overlap with arXiv:2003.06155

References in corpus (4)

• A Hopf's lemma and a strong minimum principle for the fractional $p$-Laplacian
• Existence and concentration results for some fractional Schrödinger equations in ${\mathbb{R}}^N$ with magnetic fields
• Concentrating solutions for a class of nonlinear fractional Schrödinger equations in ${\mathbb{R}}^N$
• Spectrum of the fractional $p-$Laplacian in ${\mathbb{R}}^N$ and decay estimate for positive solutions of a Schrödinger equation