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Periodic solution of a Mathieu-Duffing type equation. (English) Zbl 0881.34064

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:

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.)
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