Existence and Structure of Entire Large Positive Radial Solutions for a Class of Quasilinear Elliptic Systems

Abstract

In this paper, we consider the problem for the existence of the entire positive radial solutions of quasilinear elliptic system  div(A1(|∇u|)∇u) = F (|x|, u, v), x ∈ R , div(A2(|∇v|)∇v) = G(|x|, u, v), x ∈ R , lim |x|→∞ u(x) = +∞, lim |x|→∞ v(x) = +∞, x ∈ R . And, we also consider the following quasilinear elliptic system:  div(A1(|∇u|)∇u) = p(|x|)g(v), x ∈ R , div(A2(|∇v|)∇v) = q(|x|)f(u), x ∈ R , lim |x|→∞ u(x) = +∞, lim |x|→∞ v(x) = +∞, x ∈ R . Using the theory of ordinary differential equation, iteration method and comparison principle, which studied the existence and structure of positive entire large radial solutions. The main results of the present paper are new and extend the previously known results.