On the radial solutions of a system with weights under the Keller--Osserman condition

TL;DR

This paper investigates the existence of positive solutions for a weighted semilinear elliptic system, establishing necessary and sufficient conditions on the weights under the Keller--Osserman condition.

Contribution

It provides a comprehensive characterization of weight conditions that guarantee solutions, advancing understanding of weighted elliptic systems.

Findings

Necessary and sufficient weight conditions identified

Existence of bounded and unbounded solutions established

Conditions under the Keller--Osserman framework clarified

Abstract

In this paper, we establish conditions on the weights that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of a semilinear elliptic system.