带梯度项的（k1, k2）型 Hessian 系统全子解的必要条件和充分条件

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-06-24 DOI:10.1063/5.0192926

Chenghua Gao, Xingyue He

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引用次数: 0

摘要

本文旨在讨论一类带梯度项的 (k1, k2) 型 Hessian 系统。在 k1 = k2 = 1 且 2 ≤ k1, k2 ≤ n 的情况下，根据不同参数的取值范围，我们得到了系统整个可接受子解存在的充分必要条件，也称为广义 Keller-Osserman 条件。在此基础上，我们还分别讨论了整个子解存在和不存在的条件。最后，我们将非线性项扩展到退化情况，并考虑上述系统正子溶液的存在条件。

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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Necessary and sufficient conditions of entire sub-solutions for a (k1, k2)-type Hessian systems with gradient terms

In this paper, we aim to discuss a class of (k1, k2)-type Hessian system with gradient terms. In the case of k1 = k2 = 1 and 2 ≤ k1, k2 ≤ n, we obtain a sufficient and necessary condition for the existence of the entire admissible sub-solution of the system according to the value range of different parameters, which is also called the generalized Keller–Osserman condition. Based on this, we also discuss the conditions of existence and non-existence of the entire sub-solution, respectively. Finally, we extend the nonlinear terms to the degenerate case and consider the condition of the existence of the positive sub-solution for the above system.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.