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Zbl 0881.34064
Esmailzadeh, E.; Nakhaie-Jazar, G.
Periodic solution of a Mathieu-Duffing type equation. (English)
[J] Int. J. Non-Linear Mech. 32, No.5, 905-912 (1997). ISSN 0020-7462

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.

MSC 2000:: *34C25 Periodic solutions of ODE
74H45 Vibrations
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
34B30 Special ODE

Keywords: periodic solution; parametric second-order ordinary differential equations; Mathieu-Duffing equation; nonlinear vibration

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