Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

A new critical curve for the Lane-Emden system

Pages: 2469 - 2479, Volume 34, Issue 6, June 2014      doi:10.3934/dcds.2014.34.2469

       Abstract        References        Full Text (394.2K)       Related Articles       

Wenjing Chen - Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile (email)
Louis Dupaigne - Institut Camille Jordan UMR CNRS 5208, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France (email)
Marius Ghergu - School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland (email)

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

Keywords:  Lane-Emden system, radially symmetric solutions, stable solutions, critical curve, singular solutions.
Mathematics Subject Classification:  Primary: 35J47, 35J57; Secondary: 26D20.

Received: February 2013;      Revised: May 2013;      Available Online: December 2013.