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

Abstract

We use continuation and moving hyperplane methods to prove some existence and a priori estimates for p-Laplace systems of the form { - Δp1 u = f( v ) in Ω, u = 0 on ∂Ω, { - Δp2 v = g( u ) in Ω, v = 0 on ∂Ω, where 1 (p1 - 1)(p2 - 1). We extend results obtained in Azizieh and Clément (J. Differential Equations, 179 (2002), 213-245) where the case of a single equation was considered. © 2002 Elsevier Science (USA).