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 D pui+hi(\vert x\vert) \vert \nabla ui\vert p-1=ai(\vert x\vert ) fi(u1,u2) on RN (N\geq 3, i=1,2) where N-1\geq p>1, Dp 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).