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

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We deal with existence of entire solutions for the quasilinear elliptic system of this type Δₚuᵢ+hᵢ(|x|)| uᵢ|ᵖ⁻¹=aᵢ(|x|)fᵢ(u₁,u₂) on Rⁿ (N≥3, i=1,2) where N-1>1, Δₚ 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 improve those obtained by Xinguang Zhang and Lishan Liu, The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term, Journal of Mathematical Analysis and Applications, Volume 371, Issue 1, 1 November 2010, Pages 300-308).