Asymptotic Behavior of Singular Solution to the k-Hessian Equation with a Matukuma-Type Source

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外文摘要：This paper is concerned with radially positive solutions of the k-Hessian equation involving a Matukuma-type source Sk(D2(-φ))=|x|λ-2/(1+|x|2)λ/2φq,x∈Ω,where Sk(D2(-φ))is the k-Hessian operator,q＞k＞1,λ＞0,n＞2k,k ∈ N.and Ω is a suitable bounded do-main in Rn.It turns out that there are two different types of radially positive solutions for k＞1,i.e.,M-solution(singular at r=0)and E-solution(regular at r=0),which is distinct from the case when k=1.For 1＜q＜[(n-2+λ)k]/(n-2k),we apply an iterative approach to im-prove accuracy of asymptotic expansions of M-solution step by step to the desired extend.In contrast to the case k=1,we require a more precise range of parameters due to repeated application of Taylor expansions,which also makes asymptotic expansions need more delicate investigation.

外文关键词：

k-Hessian equationsingular solutionsasymptotic expansion

作者：

LIU Jinyu、WANG Biao、CHANG Caihong

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作者单位：

College of Science,Xi'an University of Science and Technology,Xi'an 710054,Shaanxi,China

基金：

National Natural Science Foundation of ChinaResearch startup Foundation for Talent Introduction of Xi'an University of Science and TechnologyNatural Science Basic Research Program of Shaanxi Province

项目编号：

1180143620501230412024JC-YBQN-0014

出版年：

2024

DOI：

10.1051/wujns/2024293242

武汉大学自然科学学报(英文版)

武汉大学

武汉大学自然科学学报(英文版)

CSTPCD

影响因子：0.066

ISSN：1007-1202

年,卷(期)：2024.29(3)