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(S-k(1/k)(lambda(D-2 z(1))))S-k(1/k)(lambda(D-2 z(1))) = b(|x|)phi(z(1), z(2)), x is an element of R-N, G(S-k(1/k)(lambda(D(2)z(2))))S-k(1/k)(lambda(D(2)z(2)) = h(|x|)psi(z(1), z(2)), x is an element of R-N, 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. (c) 2020 Elsevier B.V. All rights reserved.