On the existence of radially symmetric solutions to p-k-Hessian equations and systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-02 DOI:10.1007/s13324-024-00953-8

Ling Mi, YangYang Ji

引用次数: 0

Abstract

The main objective of this paper is to study the p-k-Hessian problems. To our knowledge, the problems that has additional term in the p-k-Hessian operator were seldom studied in the literature. By means of monotone iteration method and Arzelà-Ascoli theorem, this paper investigates the existence of positive radially symmetric solutions of the following augmented p-k-Hessian equations

$$\begin{aligned} S_{k} (\lambda (D_{i}(|Du|^{p-2}D_{j}u) + \alpha I)) =a^{k}(x)f^{k}(u),~x\in \mathbb {R}^n, \end{aligned}$$

and p-k-Hessian systems

$$\begin{aligned} {\left\{ \begin{array}{ll} S_{k}(\lambda (D_{i}(|Du|^{p-2}D_{j}u) + \alpha I)) =a^{k}(x)f^{k}(v),~x\in \mathbb {R}^n,\\ S_{k}(\lambda (D_{i}(|Dv|^{p-2}D_{j}v) + \alpha I)) = b^{k}(x)g^{k}(u),~x\in \mathbb {R}^n. \end{array}\right. } \end{aligned}$$

(0.1)

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论 p-k-Hessian 方程和系统的径向对称解的存在性

本文的主要目的是研究 p-k-Hessian 问题。据我们所知，文献中很少研究 p-k-Hessian 算子中有附加项的问题。本文通过单调迭代法和 Arzelà-Ascoli 定理，研究了以下增强 p-k-Hessian 方程 $$\begin{aligned} 的正径向对称解的存在性S_{k}(\lambda (D_{i}(|Du|^{p-2}D_{j}u) + \alpha I)) =a^{k}(x)f^{k}(u),~x\in \mathbb {R}^n, \end{aligned}$$ 和 p-k-Hessian 系统 $$\begin{aligned} {left\{ \begin{array}{ll}S_{k}(\lambda (D_{i}(|Du|^{p-2}D_{j}u) + \alpha I)) =a^{k}(x)f^{k}(v),~x\in \mathbb {R}^n,\ S_{k}(\lambda (D_{i}(|Dv|^{p-2}D_{j}v) + \alpha I)) = b^{k}(x)g^{k}(u),~x\in \mathbb {R}^n.\end{array}\right.}\end{aligned}$$(0.1)

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.