# Symmetry and monotonicity properties of singular solutions to some cooperative semilinear elliptic systems involving critical nonlinearities

## TL;DR

This paper studies the symmetry and monotonicity of positive singular solutions to certain cooperative semilinear elliptic systems with critical nonlinearities, using the moving plane method in bounded and unbounded domains.

## Contribution

It establishes symmetry and monotonicity properties for solutions of elliptic systems with critical nonlinearities, extending analysis to unbounded domains.

## Key findings

- Positive singular solutions exhibit symmetry and monotonicity.
- The moving plane method effectively proves qualitative properties.
- Results apply to both bounded and unbounded domains.

## Abstract

We investigate qualitative properties of positive singular solutions of some elliptic systems in bounded and unbounded domains. We deduce symmetry and monotonicity properties via the moving plane procedure. Moreover, in the unbounded case, we study some cooperative elliptic systems involving critical nonlinearities in $\mathbb{R}^n$.