The period function of potential systems of polynomials with real zeros (Q843109)

This paper focuses on the potential system of the form \[ x''(t)+g(x)=0, \] where \(g(x)\) is a polynomial whose roots are all real, and explores the analytic behaviors of the period function of period annuli of the potential system such as the convexity, monotonicity and number of critical points. As application, the authors provide a purely analytical and shorter proof of a result for the case \(\deg g=4\) obtained by means of computer algebra in [\textit{C. Li, K. Lu}, Nonlinearity 21, No.~3, 465--483 (2008; Zbl 1142.34016)].