Monotonicity of the period map for the equation $-\varphi''+\varphi-\varphi^{k}=0$
Dynamical Systems
2024-05-15 v4 Classical Analysis and ODEs
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 , where 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.
Keywords
Cite
@article{arxiv.2212.07561,
title = {Monotonicity of the period map for the equation $-\varphi''+\varphi-\varphi^{k}=0$},
author = {Fábio Natali and Giovana Alves},
journal= {arXiv preprint arXiv:2212.07561},
year = {2024}
}
Comments
The correction of a small imperfection in the proof of Lemma 3.3 has been made. Accepted for publication in Monatshefte f\"ur Mathematik (2024)