Existence and concentration results for some fractional Schrödinger equations in ${\mathbb{R}}^N$ with magnetic fields

Abstract

We consider some nonlinear fractional Schrödinger equations with magnetic field and involving continuous nonlinearities having subcritical, critical or supercritical growth. Under a local condition on the potential, we use minimax methods to investigate the existence and concentration of nontrivial weak solutions.

arXiv admin note: text overlap with arXiv:1807.07444

References in corpus (1)

• Kato's Inequality for Magnetic Relativistic Schrödinger Operators

Cited by in corpus (6)

• Multiplicity and concentration of solutions for a fractional Kirchhoff equation with magnetic field and critical growth
• Concentrating bounded states for fractional Schrödinger-Poisson system involving critical Sobolev exponent
• Maz'ya-Shaposhnikova formula in Magnetic Fractional Orlicz-Sobolev spaces
• Multiplicity and concentration results for local and fractional NLS equations with critical growth
• Concentration phenomena for fractional magnetic NLS equations
• On degenerate fractional Schrödinger-Kirchhoff-Poisson equations with upper critical nonlinearity and electromagnetic fields