Monotonicity of the period of a nonlinear oscillator (Q276720)

This paper revisits the problem of monotonicity of the period function for the differential equation NEWLINE\[NEWLINEu''-u+u^p=0.NEWLINE\]NEWLINE The authors give a simple proof of recent results of Miyamoto and Yagasaki. The starting point of this study is the so-called Chicone's criterion which was also crucially used in Miyamoto and Yagasaki's works. However, the new idea in this paper, as I understand, is to employ a potential shift and a change of variables. Then, the authors prove the desired result by considering the monotonicity of a function obtained from the potential shift and variables change.