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).

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