Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in ${\mathbb{R}}^2$

Abstract

We study the following singularly perturbed nonlocal Schrödinger equation $$ -\vr^2Δu +V(x)u =\vr^{μ-2}\Big[\frac{1}{|x|^μ}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, $$ where $V(x)$ is a continuous real function on ${\mathbb{R}}^2$, $F(s)$ is the primitive of $f(s)$, $0<\mu <2$ and $\vr$ is a positive parameter. Assuming that the nonlinearity $f(s)$ has critical exponential growth in the sense of Trudinger-Moser, we establish the existence and concentration of solutions by variational methods.

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References in corpus (1)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics

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