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doi:10.3785/j.issn.1008-9497.2023.04.005

Journal of Zhejiang University (Science Edition)

2023, Vol. 50

Issue (4): 424-428 DOI: 10.3785/j.issn.1008-9497.2023.04.005

Mathematics and Computer Science

The uniqueness and convergence of

k

-admissible solutions for a class of

k

-Hessian equations

Xingyue HE(

),Huanhuan DING

College of Mathematics and Statistics，Northwest Normal University，Lanzhou 730070，China

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Abstract

A class of coupled $k$ -Hessian equations is considered. Firstly, by using the $u 0$ -sublinear theorem, it is proved that the equation has at most one radial $k$ -admissible solution under the super-linear and sub-linear conditions. The uniqueness of radial k-admissible solution is verified by a numerical example. Finally, by incorporate with the monotone iterative technique, the uniform convergence of the solution is also discussed.

Key words： k-Hessian equation radial k-admissible solution u0-sublinear theorem monotone iterative technique

Received: 19 September 2022 Published: 17 July 2023

CLC:

O 175.8

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Cite this article:

Xingyue HE, Huanhuan DING. The uniqueness and convergence of $k$ -admissible solutions for a class of $k$ -Hessian equations. Journal of Zhejiang University (Science Edition), 2023, 50(4): 424-428.

URL:

https://www.zjujournals.com/sci/EN/Y2023/V50/I4/424

一类k-Hessian方程k-允许解的唯一性和收敛性

首先，运用 $u 0$ -次线性定理，证明了一类耦合 $k$ -Hessian方程在超线性和次线性情形下，至多存在一个径向 $k$ -允许解；其次，用数值例子验证了径向 $k$ -允许解的唯一性；最后，运用单调迭代技巧，讨论了 $k$ -允许解的一致收敛性。

关键词： k-Hessian方程, 径向k-允许解, u0-次线性定理, 单调迭代技巧


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