Nonlinear Analysis 56 (2004) 1007–1010 www.elsevier.com/locate/na An existence result on positive solutions for a class of p-Laplacian systems D.D. Hai, R. Shivaji ∗ Department of Mathematics, Mississippi State University, Mississippi State, MS 39762, USA Received 15 August 2003; accepted 31 October 2003 Abstract Consider the system -pu = f(v) in ; -pv = g(u) in ; u = v =0 on @; where pz = div(|∇z| p-2 ∇z);p¿ 1,  is a positive parameter, and  is a bounded domain in R N with smooth boundary @. We prove the existence of a large positive solution for  large when lim x→∞ f(M (g(x) 1=(p-1) ) x p-1 =0 for every M¿ 0. In particular, we do not assume any sign conditions on f(0) or g(0). ? 2003 Elsevier Ltd. All rights reserved. Keywords: p-Laplacian systems; Semipositone; Positive solutions 1. Introduction Consider the boundary value problem (I)        - p u = f(v) in ; - p v = g(u) in ; u = v =0 on @; ∗ Corresponding author. E-mail address: shivaji@ra.msstate.edu (R. Shivaji). 0362-546X/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.na.2003.10.024