# Uniqueness of minimal energy solutions for a semilinear problem involving the fractional laplacian

## TL;DR

This paper investigates the uniqueness of minimal energy solutions for a fractional Laplacian semilinear problem, particularly in small domains, extending classical Neumann problem concepts to fractional settings.

## Contribution

It establishes the uniqueness of minimal energy solutions for fractional Laplacian problems in small domains, a novel extension of classical Neumann problem results.

## Key findings

- Uniqueness of minimal energy solutions in small domains
- Extension of classical Neumann problem concepts to fractional Laplacian
- Results applicable to fractional semilinear problems

## Abstract

In this paper we study a semilinear problem for the fractional laplacian that are the counterpart of the Neumann problems in the classical setting. We show uniqueness of minimal energy solutions for small domains.