方程 $$-\varphi ''+\varphi -\varphi ^{k}=0$$ 的周期图的单调性

Monatshefte für Mathematik Pub Date : 2024-04-04 DOI:10.1007/s00605-024-01969-9

Giovana Alves, Fábio Natali

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引用次数: 0

摘要

在本文中，我们针对方程 $-\varphi ''+\varphi -\varphi ^{k}=0$的某些周期解（其中 $k>1$是实数）的能级建立了周期图的单调性。我们提出了一种新方法，利用周期解周围相应线性化算子的谱信息以及与 Floquet 理论相关的工具来证明这一性质。

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$Monotonicity of the period map for the equation $$-\varphi ''+\varphi -\varphi ^{k}=0$$$

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Monotonicity of the period map for the equation $$-\varphi ''+\varphi -\varphi ^{k}=0$$

In this paper, we establish the monotonicity of the period map in terms of the energy levels for certain periodic solutions of the equation $-\varphi ''+\varphi -\varphi ^{k}=0$, where $k>1$ is a real number. We present a new approach to demonstrate this property, utilizing spectral information of the corresponding linearized operator around the periodic solution and tools related to Floquet theory.

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Monatshefte für Mathematik

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