A new critical curve for the Lane-Emden system

TL;DR

This paper introduces a new critical curve that precisely characterizes the existence of stable positive radially symmetric solutions for the Lane-Emden system in Euclidean space.

Contribution

The authors derive an optimal critical curve for the existence of stable solutions to the Lane-Emden system, advancing understanding of solution behavior.

Findings

New critical curve for solution existence

Optimal description of stability regions

Enhanced understanding of Lane-Emden system solutions

Abstract

We study stable positive radially symmetric solutions for the Lane-Emden system $-\Delta u=v^p$ in $\R^N$, $-\Delta v=u^q$ in $\R^N$, where $p,q\geq 1$. We obtain a new critical curve that optimally describes the existence of such solutions.