Electron. J. Diff. Eqns., Vol. 2009(2009), No. 71, pp. 1-7.

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

Xudong Shang, Jihui Zhang

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 1, 2009.
Math Subject Classifications: 34A34, 34B18.
Key Words: p-Laplacian system; positive solutions; operator of type $(S)_+$.

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Xudong Shang
Department of Mathematics, Nanjing Normal University Taizhou College
Taizhou 225300, Jiangsu, China
email: xudong-shang@163.com
Jihui Zhang
Institute of Mathematics, School of Mathematics and Computer Sciences
Nanjing Normal University, Nanjing 210097, Jiangsu, China
email: jihuiz@jlonline.com

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