An existence result for a quasilinear system with gradient term under the Keller Osserman conditions

Abstract

We use some new technical tools to obtain the existence of entire solutions for the quasilinear elliptic system of type ∆pui + hi (|x|)|∇ui| p−1 = ai (|x|) fi (u1, u2) on R N (N ≥ 3, i = 1, 2 ) where N − 1 ≥ p > 1, ∆p is the p-Laplacian operator, and hi , ai , fi are suitable functions. The results of this paper supplement the existing results in the literature and complete those obtained by Jesse D Peterson and Aihua W Wood (Large solutions to non-monotone semilinear elliptic systems, Journal of Mathematical Analysis and Applications, Volume 384, pages 284 292, 2011).