Fractional NLS equations with magnetic field, critical frequency and critical growth

2016/06/27 by Binlin Zhang, Marco Squassina, Binlin, Zhang +3
Mathematics · #35B33 #35J62 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35R11 #Secondary 35A15

paper · pdf · doi:10.48550/arxiv.1606.08471

openalex publication_date 2016/06/27 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to the study of a singularly perturbed fractional Schrödinger equations involving critical frequency and critical growth in the presence of a magnetic field. By using variational methods, we obtain the existence of mountain pass solutions u_ε which tend to the trivial solution as ε→0. Moreover, we get infinitely many solutions and sign-changing solutions for the problem in absence of magnetic effects under some extra assumptions.

Citations

• Ground states for fractional magnetic operators

Related

• Fractional magnetic Schrödinger equations with potential vanishing at infinity and supercritical exponents
• Nonlinear fractional magnetic Schrödinger equation: existence and multiplicity
• Existence and concentration of nontrivial solutions for a fractional magnetic Schrödinger-Poisson type equation
• Multiplicity results for fractional magnetic problems involving\n exponential growth
• Nonlocal Schrödinger-Kirchhoff equations with external magnetic field