An Existence Theorem for a Class of Nonlinear Dirichlet Systems (communicated by Vicentiu Radulescu)

In this article, we discuss the existence of weak solution for the nonlinear system  − div ( h1(|∇u|) |∇u|p−2∇u ) = f(x, u, v) in Ω, − div ( h2(|∇v|) |∇v|p−2∇v ) = g(x, u, v) in Ω, u = v = 0 on ∂Ω, where Ω is a bounded smooth open set in Rn, p ≥ 2 and h1, h2 ∈ C(R,R). Using variational methods, under suitable assumptions on the nonlinearities, we show the existence of weak solution.