具有 L2 临界指数的基尔霍夫方程的归一化解

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-07-25 DOI:10.1063/5.0180748

Changlin Liu, Ying Lv, Zengqi Ou

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引用次数: 0

摘要

本文研究了非线性基尔霍夫型方程-a+b∫RN|∇u|2dxΔu=λu+|u|p-2u+|u|q-2u在RN中的归一化解的非存在性和存在性，其中N = 1, 2, 3, a, b &；gt; 0 为常数，q=2+8N 为基尔霍夫方程的 L2 临界指数，p=2+4N 为 "局部 "方程的 L2 临界指数。

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Normalized solutions for Kirchhoff equation with L2-critical exponents

In this paper, we study the nonexistence and existence of normalized solutions for the nonlinear Kirchhoff-type equation −a+b∫RN|∇u|2dxΔu=λu+|u|p−2u+|u|q−2u in RN with prescribed L2-norm, where N = 1, 2, 3, a, b > 0 are constants, q=2+8N is L2-critical exponent to Kirchhoff-type Equation, and p=2+4N is the L2-critical exponent to the “local” equation.

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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.