一类k-Hessian方程解的存在性和渐近稳定性  

Existence and Asymptotic Behavior of Solutions of a Class of k-Hessian Equation

作　　者：张丽红 杨泽栋 王国涛 Baleanu Dumitru Zhang Lihong;Yang Zedong;Wang Guotao;Baleanu Dumitru(School of Mathematics and Computer Science,Shanxi Normal University,Shanxi Linfen O41OO4;Nonlinear Analysis and Applied Mathematics(NAAM)Research Group,Department of Mathematics,Faculty of Science,King Abdulaziz University,Saudi Arabia Jeddah 21589;Department of Mathematics,Faculty of Art and Sciences,Cankaya University,Turkey,Ankara Balgat 06530;Institute of Space Sciences,Magurele-Bucharest,Romania)

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041004 [2]Nonlinear Analysis and Applied Mathematics(NAAM)Research Group,Department of Mathematics,Faculty of Science,King Abdulaziz University,Saudi Arabia Jeddah 21589 [3]Department of Mathematics,Faculty of Art and Sciences,Cankaya University,Turkey,Ankara Balgat 06530 [4]Institute of Space Sciences,Magurele-Bucharest,Romania

出　　处：《数学物理学报（A辑）》2021年第5期1357-1371,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(11501342,12001344);山西省研究生教育创新项目基金(2020SY337)。

摘　　要：该文考虑了边界爆破k-Hessian问题Sk(λ(D^(2)z))=b(x)f(z),x∈Ω,z|■Ω=+∞,其中,Ω■R^(N)是一个严格凸的光滑有界区域.文章通过单调迭代方法、上下解方法和Karamata正则变化理论得到了k-Hessian方程径向对称正解的存在性和严格凸的爆破正解的边界渐近行为.In this paper,we consider the following boundary blow-up k-Hessian problem Sk(λ(D^(2)z))=b(x)f(z),x∈Ω,z|■Ω=+∞,whereΩ■RN is a smooth,bounded,strictly convex domain.We are concerned with the existence of the radially symmetric positive solutions of the k-Hessian equation and obtain new boundary asymptotic behavior of strictly convex blow-up positive solutions of the k-Hessian equation.Our approach mainly relies on the monotone iterative method,the upper and lower solution method and Karamata regular variation theory.

关 键 词：渐近稳定性 k-Hessian方程 径向正解 Keller-Osserman条件 Karamata正则变化理论 

分 类 号：O175[理学—数学]