Radial solutions of a nonlinear k-Hessian system involving a nonlinear operator

Abstract

In this paper, we consider the following nonlinear k-Hessian system{G(Sk1k(λ(D2z1)))Sk1k(λ(D2z1))=b(|x|)φ(z1,z2),x∈RN,G(Sk1k(λ(D2z2)))Sk1k(λ(D2z2))=h(|x|)ψ(z1,z2),x∈RN,where G is a nonlinear operator. This paper first proves the existence of the entire positive bounded radial solutions, and secondly gives the existence and non-existence conditions of the entire positive blow-up radial solutions. Finally, we give some examples to illustrate our results.