A new critical curve for the Lane-Emden system

Wenjing Chen; Louis Dupaigne; Marius Ghergu

doi:10.3934/dcds.2014.34.2469

Article Contents

2014, Volume 34, Issue 6: 2469-2479. Doi: 10.3934/dcds.2014.34.2469

This issue Previous Article A symmetry result for the Ornstein-Uhlenbeck operator Next Article On the converse problem for the Gross-Pitaevskii equations with a large parameter

A new critical curve for the Lane-Emden system

1.
Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago
2.
Institut Camille Jordan UMR CNRS 5208, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex
3.
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4

Received: February 2013

Revised: May 2013

Published: June 2014

Abstract / Introduction Related Papers Cited by

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.

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Mathematics Subject Classification: Primary: 35J47, 35J57; Secondary: 26D20.

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