Upper and Lower Solution Method for a Singular k-Hessian System With Augmented Gradient Term

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-08-03 DOI:10.1002/mma.70024

Xinguang Zhang, Peng Chen, Lishuang Li, Yonghong Wu, Benchawan Wiwatanapataphee, Ying Wang

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引用次数: 0

Abstract

In this paper, we focus on the existence of solutions for a singular $k$ -Hessian system with augmented gradient term. By using a radial symmetric transformation and constructing a pair of suitable upper and lower solutions of the singular $k$ -Hessian system, the existence and the asymptotic estimate of the solution for the system are established under the case where the nonlinearities $f, g$ are allowed to have stronger singularity on the space variables. In particular, the nonsingular case is also considered and a sharp result is derived.

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一类具有增广梯度项的奇异k-Hessian系统的上下解法

本文研究了一类具有增广梯度项的奇异k $$ k $$ -Hessian系统解的存在性。利用径向对称变换，构造奇异k $$ k $$ -Hessian系统的一对合适的上下解，给出了该系统在非线性f，G $$ f,g $$在空间变量上允许有更强的奇异性。特别地，我们还考虑了非奇异情况，并得到了一个明显的结果。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.