Abstract
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.
基金项目
National Natural Science Foundation of China(11801436)
Research startup Foundation for Talent Introduction of Xi'an University of Science and Technology(2050123041)
Natural Science Basic Research Program of Shaanxi Province(2024JC-YBQN-0014)
NETL
NSTL
万方数据