Multiplicity and concentration results for a fractional Schrödinger-Poisson type equation with magnetic field

Abstract

This paper is devoted to the study of fractional Schrödinger-Poisson type equations with magnetic field of the type \begin{equation*} \varepsilon^{2s}(-Δ)_{A/\varepsilon}^{s}u+V(x)u+\varepsilon^{-2t}(|x|^{2t-3}*|u|^{2})u=f(|u|^{2})u \quad \mbox{ in } \mathbb{R}^{3}, \end{equation*} where $\epsilon >0$ is a parameter, $s,t\in (0,1)$ are such that $2s+2t>3$, $A:{\mathbb{R}}^3\to {\mathbb{R}}^3$ is a smooth magnetic potential, $(-\Delta {)}_A^s$ is the fractional magnetic Laplacian, $V:{\mathbb{R}}^3\to \mathbb{R}$ is a continuous electric potential and $f:\mathbb{R}\to \mathbb{R}$ is a $C^1$ subcritical nonlinear term. Using variational methods, we obtain the existence, multiplicity and concentration of nontrivial solutions for $\epsilon >0$ small enough.

References in corpus (3)

• Singular perturbation by bending for an adhesive obstacle problem
• Positive semiclassical states for a fractional Schrödinger-Poisson system
• Fractional Schrödinger-Poisson-Slater system in one dimension

Cited by in corpus (3)

• Maz'ya-Shaposhnikova formula in Magnetic Fractional Orlicz-Sobolev spaces
• Nonlinear Perturbations of a periodic magnetic Choquard equation with Hardy-Littlewood-Sobolev critical exponent
• On degenerate fractional Schrödinger-Kirchhoff-Poisson equations with upper critical nonlinearity and electromagnetic fields