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2005, 2005(Special): 510-517. doi: 10.3934/proc.2005.2005.510

On lane-emden type systems

Philip Korman 1, and  Junping Shi 2,

1. 

Department Of Mathematical Sciences, University Of Cincinnati, Cincinnati Ohio 45221-0025
2. 

Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187, United States

Received  September 2004 Revised  April 2005 Published  September 2005

We consider a class of singular systems of Lane-Emden type \begin{equation} \nonumber \begin{cases} \Delta u + \la u^{p_1} v^{q_1}=0, & x\in D,\\ \Delta v + \la u^{p_2} v^{q_2}=0, & x\in D,\\ u=v=0, & x\in \partial D, \end{cases} \end{equation} with $p_1\le 0, \; p_2> 0, \; q_1> 0, \; q_2\le 0$, and $D$ a smooth domain in $\R^n$. In case the system is sublinear we prove existence of a positive solution. If $D$ is a ball in $\R^n$, we prove both existence and uniqueness of positive radially symmetric solution.
Keywords: semilinear elliptic system, uniqueness..
Mathematics Subject Classification: Primary: 35J55, 35J4.
Citation: Philip Korman, Junping Shi. On lane-emden type systems. Conference Publications, 2005, 2005 (Special) : 510-517. doi: 10.3934/proc.2005.2005.510
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