On lane-emden type systems

Pages: 510 - 517, Issue Special, August 2005

 Abstract        Full Text (120.7K)              

Philip Korman - Department Of Mathematical Sciences, University Of Cincinnati, Cincinnati Ohio 45221-0025, United States (email)
Junping Shi - Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187, United States (email)

Abstract: 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, 35J45.

Received: September 2004;      Revised: April 2005;      Published: September 2005.