Esmailzadeh, E.; Nakhaie-Jazar, G. Periodic solution of a Mathieu-Duffing type equation. (English) Zbl 0881.34064 Int. J. Non-Linear Mech. 32, No. 5, 905-912 (1997). Summary: It is found that there exist necessary and sufficient conditions for the existence of at least one periodic solution for a type of parametric second-order ordinary differential equations, known as the Mathieu-Duffing equation. The correctness of the conditions have been pointed out by Schauder’s fixed point theorem, and the validity of the assumptions has been shown by the analysis of an illustrative example in nonlinear vibration. Cited in 17 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 74H45 Vibrations in dynamical problems in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) Keywords:periodic solution; parametric second-order ordinary differential equations; Mathieu-Duffing equation; nonlinear vibration PDFBibTeX XMLCite \textit{E. Esmailzadeh} and \textit{G. Nakhaie-Jazar}, Int. J. Non-Linear Mech. 32, No. 5, 905--912 (1997; Zbl 0881.34064) Full Text: DOI