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

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).