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

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