Periodic solutions for nonlinear \(n\)th order ordinary differential equations (Q1353475)

The author extends and in a certain sense generalizes the results due to \textit{J. Andres} [J. Math. Anal. Appl. 167, No. 1, 1-11 (1992; Zbl 0762.34017)] concerning the existence of an \(\omega\)-periodic solution to the equation \[ x^{(n)}+ \sum_{j=1}^{n-1} a_j(t)x^{(n-j)}+ h(x)=p(t) \] with \(\omega\)-periodic coefficients and an \(\omega\)-periodic forcing term \(p(t)\). The regularity assumptions for \(a_j(t)\), \(j=1,\dots,n-1\), are similar, but the restriction imposed on the restoring term \(h(x)\) is only of the sign type. Thus, the growth restrictions used in the reviewer's paper are eliminated.