American Institute of Mathematical Sciences

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2009, 2009(Special): 810-817. doi: 10.3934/proc.2009.2009.810

Existence and nonexistence of positive radial solutions for quasilinear systems

Haiyan Wang 1,

1. 

Department of Mathematical Sciences & Applied Computing, Arizona State University, Phoenix, AZ 85069-7100

Received  August 2008 Revised  March 2009 Published  September 2009

The paper deals with the existence and nonexistence of positive radial solutions for the weakly coupled quasilinear system div$( | \nabla u|^{p-2}\nabla u ) + \lambda f(v)=0$, div $( | \nabla v|^{p-2}\nabla v ) + \lambda g(u)=0$ in $\B$, and $\u =v=0$ on $\partial B,$ where $p>1$, $B$ is a finite ball, $f$ and $g$ are continuous and nonnegative functions. We prove that there is a positive radial solution for the problem for various intevals of $\lambda$ in sublinear cases. In addition, a nonexistence result is given. We shall use fixed point theorems in a cone.
Keywords: p-Laplace operator, positive radial solution, cone.
Mathematics Subject Classification: Primary: 35J55, 34B15.
Citation: Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810
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