Monotonicity of the period of a non linear oscillator

TL;DR

This paper investigates the monotonicity of the period function for a specific nonlinear oscillator, providing a simplified proof of recent findings in the field.

Contribution

It offers a straightforward proof of the monotonicity property for the period of a nonlinear oscillator, building on recent research by Miyamoto and Yagasaki.

Findings

Confirmed the monotonicity of the period function for the oscillator.

Provided a simplified proof technique for existing results.

Enhanced understanding of nonlinear oscillator dynamics.

Abstract

We revisit the problem of monotonicity of the period function for the differential equation $u"-u+u^p=0$ and give a simple proof of recent results of Miyamoto and Yagasaki.