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

2011/06/21 by Dragos-Patru Covei, Dragoş-Pătru Covei, Covei, Dragos-Patru
Computer Science · Mathematics · #35J60 #35J62 #35J66 #35J92 #58J10 #58J20 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.CA #msc:35J60 #msc:35J62 #msc:35J66 #msc:35J92 #msc:58J10 #msc:58J20

paper · pdf · doi:10.48550/arxiv.1106.4109

10 pages

arxiv created 2011/06/21 · openalex publication_date 2011/06/21 · arxiv updated 2011/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with existence of entire solutions for the quasilinear elliptic system of this type Δ_pu_i+h_i(|x|)|\bigtriangledown u_i|^p-1=a_i(|x|)f_i(u₁,u₂) on R^N (N≥3, i=1,2) where N-1\geqp>1, Δ_p is the p-Laplacian operator and h_i, a_i, f_i 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).

Related

• Singular Quasilinear Elliptic Systems With Gradient Dependence
• Existence results for a quasilinear elliptic problem with a gradient term via shooting method
• The Keller-Osserman type conditions for the study of existence of entire radial solutions to a semilinear elliptic system
• Singular quasilinear elliptic systems involving gradient terms
• Existence and nonexistence of positive solutions of quasi-linear elliptic equations with gradient terms