In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z...In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z2),x∈R^(N),where G is a nonlinear operator and Sk(λ(D^(2)z))stands for the k-Hessian operator.We first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system ifφ(|x|,z1,z2)=b(|x|)φ(z1,z2)andψ(|x|,z1,z2)=h(|x|)ψ(z1).Moreover,with the help of the monotone iterative method,some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearitiesψ,φare given,which improve and extend many previous works.展开更多
基金Supported by the National Natural Science Foundation of China(11501342,12001344).
文摘In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z2),x∈R^(N),where G is a nonlinear operator and Sk(λ(D^(2)z))stands for the k-Hessian operator.We first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system ifφ(|x|,z1,z2)=b(|x|)φ(z1,z2)andψ(|x|,z1,z2)=h(|x|)ψ(z1).Moreover,with the help of the monotone iterative method,some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearitiesψ,φare given,which improve and extend many previous works.
