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arXiv · 2212.07561

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

Fábio Natali·Giovana Alves
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Abstract

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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Fábio Natali, Giovana Alves. 2022-12-15. Monotonicity of the period map for the equation $-\varphi''+\varphi-\varphi^{k}=0$. https://arxiv.org/abs/2212.07561

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