Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 71, pp. 1-7.

Title: Existence of positive solutions for quasilinear elliptic systems
       involving the p-Laplacian

Author: Xudong Shang (Nanjing Normal Univ., Jiangsu, China)
        Jihui Zhang  (Nanjing Normal Univ., Jiangsu, China)

Abstract:
 In this article, we study the existence of positive solutions for
 the quasilinear elliptic system
 $$\displaylines{
 -\Delta_{p}u = f(x,u,v) \quad x \in \Omega ,\cr
 -\Delta_{p}v = g(x,u,v) \quad x \in \Omega ,\cr
 u = v = 0 \quad x \in \partial\Omega.
 }$$
 Using degree theoretic arguments based on the degree map for
 operators of type $(S)_{+}$, under suitable assumptions on the
 nonlinearities,  we prove the existence of positive weak solutions.
 
Submitted March 6, 2009. Published June 01, 2009.
Math Subject Classifications: 34A34, 34B18.
Key Words: p-Laplacian system; positive solutions; 
           operator of type $(S)_+$.