# Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well

## TL;DR

This paper investigates the existence and behavior of least energy solutions for a fractional Choquard equation with a potential well, showing solutions localize near the well as the parameter increases.

## Contribution

It establishes the existence and asymptotic localization of least energy solutions for fractional Choquard equations with potential wells using variational methods.

## Key findings

- Solutions exist for large mbda.
- Solutions localize near the potential well as mbda increases.
- The paper provides conditions for existence and localization of solutions.

## Abstract

In this paper, we are concerned with the existence and asymptotic behavior of least energy solutions for following nonlinear Choquard equation driven by fractional Laplacian $$(-\Delta)^{s} u+\lambda V(x)u=(I_{\alpha}\ast F(u))f(u) \ \ in \ \ R^{N},$$ where $N> 2s$, $ (N-4s)^{+}<\alpha< N$, $\lambda$ is a positive parameter and the nonnegative potential function $V(x)$ is continuous. By variational methods, we prove the existence of least energy solution which localize near the potential well $int (V^{-1}(0))$ as $\lambda$ large enough.