This paper mainly studies the following Monge-Ampère type systems{det^(1/n)(ΔuI-D^(2)u)=p(|x|)f(v),x∈R^(n),det^(1/n)(ΔvI-D^(2)v)=q(|x|)g(u),x∈R^(n).The existence of entire radial solutions is obtained by usin...This paper mainly studies the following Monge-Ampère type systems{det^(1/n)(ΔuI-D^(2)u)=p(|x|)f(v),x∈R^(n),det^(1/n)(ΔvI-D^(2)v)=q(|x|)g(u),x∈R^(n).The existence of entire radial solutions is obtained by using monotone iteration method and Arzelà-Ascoli theorem.These results generalize the classical Keller-Osserman condition to fully nonlinear systems.展开更多
In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution...In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou（existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters,Volume 50, December 2015, Pages 48–55）.展开更多
文摘This paper mainly studies the following Monge-Ampère type systems{det^(1/n)(ΔuI-D^(2)u)=p(|x|)f(v),x∈R^(n),det^(1/n)(ΔvI-D^(2)v)=q(|x|)g(u),x∈R^(n).The existence of entire radial solutions is obtained by using monotone iteration method and Arzelà-Ascoli theorem.These results generalize the classical Keller-Osserman condition to fully nonlinear systems.
文摘In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou（existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters,Volume 50, December 2015, Pages 48–55）.
