Multiplicity and concentration results for a fractional Choquard equation via penalization method

Abstract

This paper is devoted to the study of the following fractional Choquard equation $$ \varepsilon^{2s}(-Δ)^{s} u + V(x)u = \varepsilon^{μ-N}\left(\frac{1}{|x|^μ}*F(u)\right)f(u) \mbox{ in } \mathbb{R}^{N}, $$ where $\epsilon >0$ is a parameter, $s\in (0,1)$, $N>2s$, $(-\Delta {)}^s$ is the fractional Laplacian, $V$ is a positive continuous potential with local minimum, $0<\mu <2s$, and $f$ is a superlinear continuous function with subcritical growth. By using the penalization method and the Ljusternik-Schnirelmann theory, we investigate the multiplicity and concentration of positive solutions for the above problem.

arXiv commentarXiv admin note: text overlap with arXiv:1711.03625

References in corpus (7)

• An extension problem related to the fractional Laplacian
• Fractional Schrodinger equation
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• A guide to the Choquard equation
• Ground state solutions for nonlinear fractional Schrödinger equations in ${\mathbb{R}}^N$
• Ground state solutions for non-autonomous fractional Choquard equations
• Multiplicity of positive solutions for a class of fractional Schrödinger equations via penalization method

Cited by in corpus (4)

• Sign-changing solutions for a class of zero mass nonlocal Schrödinger equations
• Multiple and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent
• Existence of solutions for critical Choquard problem with singular coefficients
• On the multiplicity and concentration of positive solutions for a $p$-fractional Choquard equation in ${\mathbb{R}}^N$