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Zbl 1135.34316
On the stability and the periodicity properties of solutions of a certain third order nonlinear differential equation.
(English)
[J] Acta Math. Acad. Paedagog. Nyházi. (N.S.) 23, No. 2, 149-159 (2007). ISSN 1786-0091/e

Summary: The object of this paper is to give sufficient conditions for the existence of bounded solutions that are globally exponentially stable, periodic and almost periodic, for a certain third-order non-linear differential equation. A matrix inequality is obtained and proved to satisfy a generalized frequency domain inequality of {\it V. A. Yakubovich} [Sov. Math., Dokl. 6, 98--101 (1965; Zbl 0142.36301)] through the frequency domain technique.
MSC 2000:
*34C11 Qualitative theory of solutions of ODE: Growth, etc.
34C25 Periodic solutions of ODE
34D20 Lyapunov stability of ODE

Keywords: periodic solutions; almost periodic solutions; bounded solutions; exponential stability; frequency domain

Citations: Zbl 0142.36301

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