# Existence of solutions for a semirelativistic Hartree equation with unbounded potentials

## TL;DR

This paper proves the existence of solutions for a semirelativistic Hartree equation with unbounded potentials, expanding the understanding of such equations under less restrictive growth conditions.

## Contribution

It establishes existence results for solutions to a semirelativistic Hartree equation with unbounded potential functions, a case not previously well-addressed.

## Key findings

- Existence of solutions under unbounded potential conditions
- Applicable to potentials with specific growth assumptions
- Extends previous results to more general potential functions

## Abstract

We prove the existence of a solution to the semirelativistic Hartree equation $$\sqrt{-\Delta+m^2}u+ V(x) u = A(x)\left( W * |u|^p \right) |u|^{p-2}u $$ under suitable growth assumption on the potential functions $V$ and $A$. In particular, both can be unbounded from above.