Existence and a priori estimates for positive solutions of p-Laplace systems

We use continuation and moving hyperplane methods to prove some existence and a priori estimates for p-Laplace systems of the form -Delta(p1)u = f(\v\) in Omega, u = 0 on partial derivativeOmega, -Delta(p2)v - q(\u\) in Omega, v = 0 on partial derivativeOmega, where 1 < p(1), p(2) < N, Omega subset of R-N is bounded and convex, and f, g: R --> R+ are nondecreasing locally Lipschitz continuous functions satisfying C-1\s\(q1) less than or equal to f(s) less than or equal to C-2\s\(q), D-1\s\(q2) less than or equal to g(s) less than or equal to D-2\s\q(2) Vs is an element of R+ for some positive constants C-1, C-2, D-1, D-2 and q(1)q(2) > (p(1) - 1)(p(2) - 1). We extend results obtained in Azizieh and Cement (J. Differential Equations, 179 (2002), 213245) where the case of a single equation was considered. (C) 2002 Elsevie, Science (USA).