Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 57, pp. 1-18. Title: Existence of solutions for a system of elliptic partial differential equations Author: Robert Dalmasso (Lab. Jean Kuntzmann, Grenoble Cedex, France) Abstract: In this article, we establish the existence of radial solutions for a system of nonlinear elliptic partial differential equations with Dirichlet boundary conditions. Also we discuss the question of uniqueness, and illustrate our results with examples. Submitted April 25, 2011. Published May 04, 2011. Math Subject Classifications: 35J57, 34B18. Key Words: Nonlinear systems; shooting method; positive radial solutions.