Symmetric positive solutions to nonlinear Choquard equations with potentials

TL;DR

This paper proves the existence of symmetric positive solutions for nonlinear Choquard equations with potentials that are invariant under certain symmetries, covering various nonlinearities including physically relevant cases.

Contribution

It establishes existence results for symmetric positive solutions to Choquard equations with invariant potentials, extending to different nonlinear exponents including the physically significant case.

Findings

Existence of symmetric positive solutions under invariant potentials

Results include physically relevant nonlinearities

Solutions inherit the symmetry of the potential

Abstract

Existence results for a class of Choquard equations with potentials are established. The potential has a limit at infinity and it is taken invariant under the action of a closed subgroup of linear isometries of $\mathbb{R}^N$. As a consequence, the positive solution found will be invariant under the same action. Power nonlinearities with exponent greater or equal than two or less than two will be handled. Our results include the physical case.