Periodic solutions for some ordinary differential equations involving stability (Q5945661)

\textit{F. Cong} [Nonlinear Anal., Theory Methods Appl. 32, No. 6, 787--793 (1998; Zbl 0980.34040)] studied the uniqueness and existence of periodic solutions to the \(2k\)th-order differential equation NEWLINE\[NEWLINEx^{(2k)}+ \sum^{k-1}_{j=1} \alpha_j x^{(2j)}+ (-1)^{k+ 1} f(t,x)= p(t)= p(t+ 2\pi),\quad x\in\mathbb{R}^n,NEWLINE\]NEWLINE under various stated conditions on \(f\). The authors prove the existence theorem by an alternative method which uses a global inverse function theorem. The approach is also used on the scalar Duffing equation is also used on the scalar Duffing equation NEWLINE\[NEWLINEx''+ f(t,x)= p(t)= p(t+ 2\pi),\quad x\in\mathbb R,NEWLINE\]NEWLINE investigated by \textit{H. Wang} and \textit{Y. Li} [ibid. 24, No. 7, 961--979 (1995; Zbl 0828.34030)].