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.

arXiv comment15 pages

References in corpus (9)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Existence of groundstates for a class of nonlinear Choquard equations
• Multiple solutions to a magnetic nonlinear Choquard equation
• Limiting Bourgain-Brezis estimates for systems: theme and variations
• Semi-classical states for the Choquard equation
• Uniqueness of Ground States for Pseudo-Relativistic Hartree Equations
• Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains
• Semiclassical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities
• Ground states for semi-relativistic Schrödinger-Poisson-Slater energies

Cited by in corpus (10)

• Multiplicity and concentration results for a fractional Choquard equation via penalization method
• Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well
• Multiple and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent
• Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities
• Existence of solutions for critical Choquard problem with singular coefficients
• Saddle solutions for the fractional Choquard equation
• Singular doubly nonlocal elliptic problems with Choquard type critical growth nonlinearities
• Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity
• Singular Fractional Choquard Equation with a Critical Nonlinearity and a Radon measure
• On a class of mixed Choquard-Schrödinger-Poisson system