Existence of periodic solutions for an \(n\)th order differential equation with nonlinear restoring term and time-variable coefficients (Q1197421)

The author investigates the \(\omega\)-periodic solutions of the equation \(x^{(n)}+\sum_{j=1}^{n-1} a_ j(t)x^{(n-j)}+h(x)=p(t)\) (\(n>3\)), where the coefficients \(a_ j(t)\in C^ \kappa\), \(\kappa=\max\{[j/2]\), \(n-j-1\}\), and the forcing term \(p(t)\in C\) are \(\omega\)-periodic, and the restoring term \(h(x)\) is continuously differentiable on the whole real axis.