Ground state solutions for non-autonomous fractional Choquard equations

Abstract

We consider the following nonlinear fractional Choquard equation, \begin{equation}\label{e:introduction} \begin{cases} (-Δ)^{s} u + u = (1 + a(x))(I_α\ast (|u|^{p}))|u|^{p - 2}u\quad\text{ in }\mathbb{R}^N,\\ u(x)\to 0\quad\text{ as }|x|\to \infty, \end{cases} \end{equation} here $s\in (0,1)$, $\alpha \in (0,N)$, $p\in [2,\infty )$ and $\frac{N-2s}{N+\alpha }<\frac{1}{p}<\frac{N}{N+\alpha }$. Assume ${\lim }_{|x|\to \infty }a(x)=0$ and satisfying suitable assumptions but not requiring any symmetry property on $a(x)$, we prove the existence of ground state solutions.

15 pages

References in corpus (2)

• Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
• Semiclassical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities

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