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 $(S)_+$.