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

TL;DR

This paper establishes the existence of entire solutions for a class of quasilinear elliptic systems with gradient terms under Keller-Osserman conditions, extending and improving previous results in the literature.

Contribution

It provides new existence results for quasilinear systems with gradient terms, generalizing prior work and under specific Keller-Osserman conditions.

Findings

Existence of solutions under Keller-Osserman conditions

Improvement over previous results by Zhang and Liu

Extension to systems involving p-Laplacian and gradient terms

Abstract

We deal with existence of entire solutions for the quasilinear elliptic system of this type {\Delta}_{p}u_{i}+h_{i}(|x|)|\bigtriangledown u_{i}|^{p-1}=a_{i}(|x|)f_{i}(u_1,u_2) on R^{N} (N\geq3, i=1,2) where N-1\geqp>1, {\Delta}_{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).