一类k-Hessian型方程和系统全局正径向k-凸解的存在性

Existence of entire positive radial k-convex solution fora class of k-Hessian type equation and system

运用单调迭代技巧和Arzel-Ascoli定理研究一类带权重的k-Hessian型方程S_(k)(D^(2)u+ηI)=p(x)f^((k)(x,-u,-v),x∈R N和系统S_(k)(D^(2)u+ηI)=p(x)f_(1)(^((k)(x,-u,-v),x∈R N,S_(k)(D^(2)v+ηI)=q(x)f_(2)^((k)(x,-u,-v),x∈R N全局正径向k-凸解的存在性及渐近性质,其中S_(k)是k-Hessian型算子,D^(2)u是u的Hessian矩阵,I是单位矩阵,η是非负常数,p,q是正权函数,f,f_(1),f_(2)是[0,∞)×(-∞,0)2上的连续函数.

By using a monotone iterative technique and the Arzel-Ascoli theorem,the existence and some asymptotic properties of entire positive radial k-convex solutions are given for a class of^((k)-Hessian type equation with weights S_(k)(D^(2)u+ηI)=p(x)f^((k)(x,-u,-v),x∈R N and system S_(k)(D^(2)u+ηI)=p(x)f^((k)1(x,-u,-v),x∈R N,S_(k)(D^(2)v+ηI)=q(x)f^((k)2(x,-u,-v),x∈R N.Where S_(k)is a k-Hessian type operator,D^(2)u is the Hessian matrix of u,I is the unit matrix,ηis a nonnegative constant,p,q are positive weight functions and f,f_(1),f_(2)are the continuous functions on[0,∞)×(-∞,0)2.