Positive bound states to nonlinear Choquard equations in the presence of nonsymmetric potentials

TL;DR

This paper proves the existence of positive solutions for a class of nonlinear Choquard equations with nonsymmetric potentials that approach a positive limit or oscillate, broadening the understanding of such equations without symmetry constraints.

Contribution

It establishes positive bound states for nonlinear Choquard equations with nonsymmetric potentials, including cases with oscillating or non-symmetric potentials, without symmetry assumptions.

Findings

Existence of positive solutions under broad potential conditions

Applicable to physical models with nonsymmetric potentials

No symmetry assumptions required for the potential

Abstract

The existence of a positive solution to a class of Choquard equations with potential going at a positive limit at infinity possibly from above or oscillating is proved. Our results include the physical case and do not require any symmetry assumptions on the potential.