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

作　　者：高承华 丁欢欢 GAO Cheng-hua;DING Huan-huan(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2023年第4期1-8,共8页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11961060);西北师范大学研究生科研资助项目(2021KYZZ01032)。

摘　　要：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.

关 键 词：k-Hessian型方程 全局正径向k-凸解 存在性 渐近性 单调迭代技巧 

分 类 号：O175.8[理学—数学]