一类具有临界频率的分数临界薛定谔-泊松系统的多重约束状态

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

Journal of Mathematical Physics Pub Date : 2024-07-01 DOI:10.1063/5.0174872

Xiaoming He, Yuxi Meng, Patrick Winkert

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引用次数: 0

摘要

本文研究分数薛定谔-泊松系统ε2s(-Δ)su+V(x)u=j|u|2s*-3u+|u|2s*-2u,ε2s(-Δ)sj=|u|2s*-1,x∈R3，其中s∈(0, 1)，ɛ &；gt; 0 是一个小参数，2s*=63-2s 是临界索波列夫指数，V∈L32s(R3) 是一个非负函数，在 R3 的某些区域可能为零，例如，在 R3 的某些区域可能为零。g.,它属于临界频率情况。通过新的全局紧凑性定理和 Lusternik-Schnirelmann 范畴理论，我们将边界解的数量与零集的拓扑结构联系起来，在零集中，对于ɛ的小值，V 达到最小值。

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Multiple bound states for a class of fractional critical Schrödinger–Poisson systems with critical frequency

In this paper we study the fractional Schrödinger–Poisson system ε2s(−Δ)su+V(x)u=ϕ|u|2s*−3u+|u|2s*−2u,ε2s(−Δ)sϕ=|u|2s*−1,x∈R3, where s ∈ (0, 1), ɛ > 0 is a small parameter, 2s*=63−2s is the critical Sobolev exponent and V∈L32s(R3) is a nonnegative function which may be zero in some regions of R3, e.g., it is of the critical frequency case. By virtue of a new global compactness lemma, and the Lusternik–Schnirelmann category theory, we relate the number of bound state solutions with the topology of the zero set where V attains its minimum for small values of ɛ.

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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.