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Note on existence of periodic solutions to the third-order nonlinear differential equation. (English) Zbl 0754.34038

The existence criteria for a periodic solution of a rather general nonautonomous third-order nonlinear differential equation are obtained via the Leray-Schauder fixed-point technique. The desired a priori estimates are performed by means of the Wirtinger-type inequalities. Various forms of restrictions imposed on the single terms of the equation under consideration are discussed.
Reviewer: J.Andres (Olomouc)

MSC:

34C25 Periodic solutions to ordinary differential equations
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References:

[1] Vlček V.: To existence of the periodic solution of a third-order nonlinear differential equation. Acta Univ. Palack. Olom., F.R.N. 1990, Math. XXIX, Tom 97 · Zbl 0754.34037
[2] Vlček V.: Periodic solutions of a parametric nonlinear third-order differential equation. Acta Univ. Palack. Olom., F.R.N., 1991, Math. XXX · Zbl 0777.34031
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