Ladeira, Luiz A. C.; Táboas, Plácido Z. Periodic solutions of the equation \(\ddot x+g(x)=E\,\cos \,t+\sigma h(t)\dot x\). (English) Zbl 0647.34034 Q. Appl. Math. 45, 429-440 (1987). In an early work W. S. Loud [Proc. US-Japan Sem. Differential Functional Equations Minneapolis, Minnesota 1967, 199-224 (1967; Zbl 0162.123)] analyzed the following equation (1) \(\ddot x+g(x)=E \cos t.\) In the present paper the authors prove existence of \(2\pi\)-periodic non- odd-harmonic solutions when (1) is perturbed by a small damping term, \(\sigma h(t)\dot x\), where \(\sigma\) is a real number h is a \(2\pi\)- periodic continuous function satisfying some generic conditions. The autonomous perturbation, \(h(t)=1\), does not satisfy these conditions, and is treated separately. The analysis relies essentially on the Lyapunov- Schmidt reduction. Reviewer: A.Boucherif MSC: 34C25 Periodic solutions to ordinary differential equations Keywords:non-odd-harmonic solutions; autonomous perturbation; Lyapunov-Schmidt reduction Citations:Zbl 0162.123 PDFBibTeX XMLCite \textit{L. A. C. Ladeira} and \textit{P. Z. Táboas}, Q. Appl. Math. 45, 429--440 (1987; Zbl 0647.34034) Full Text: DOI