Existence of groundstates for a class of nonlinear Choquard equations in the plane

Abstract

We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$-\Delta u+u=(I_{\alpha }\ast F(u))F^{\prime }(u)\text{in }{\mathbb{R}}^2,$$ where $I_{\alpha }$ is the Riesz potential of order $\alpha$ on the plane ${\mathbb{R}}^2$ under general nontriviality, growth and subcriticality on the nonlinearity $F\in C^1(\mathbb{R},\mathbb{R})$.

arXiv commentrevised version, 16 pages

References in corpus (4)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• A guide to the Choquard equation
• Existence of groundstates for a class of nonlinear Choquard equations
• Interpolation inequalities between Sobolev and Morrey-Campanato spaces: A common gateway to concentration-compactness and Gagliardo-Nirenberg interpolation inequalities

Cited by in corpus (5)

• Groundstates of the Choquard equations with a sign-changing self-interaction potential
• Normalized solutions for a Choquard equation with exponential growth in ${\mathbb{R}}^2$
• Positive solutions with prescribed mass for a planar Choquard equation with critical growth
• On a class of singular Hamiltonian Choquard-type elliptic systems with critical exponential growth
• Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree-Fock theory