# Positive solutions for non-variational fractional elliptic systems with negative exponents

## TL;DR

This paper investigates the existence, nonexistence, and uniqueness of positive solutions for strongly coupled non-variational fractional elliptic systems with negative exponents, extending previous results to fractional operators.

## Contribution

It extends the analysis of positive solutions to fractional elliptic systems with negative exponents, focusing on existence, nonexistence, and uniqueness in the fractional setting.

## Key findings

- Established conditions for existence of positive solutions.
- Identified scenarios leading to nonexistence.
- Proved uniqueness of solutions under certain conditions.

## Abstract

In this paper, we study strongly coupled elliptic systems in non-variational form with negative exponents involving fractional Laplace operators. We investigate the existence, nonexistence, and uniqueness of the positive classical solution. The results obtained here are a natural extension of the results obtained by Ghergu (2010), for the fractional case.