Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 23, No. 2, pp. 149-159 (2007)

On the stability and the periodicity properties of solutions of a certain third order nonlinear differential equation

Anthony Uyi Afuwape, Olufemi Adeyinka Adesina and Ebosele Peter Ebiendele

Obafemi Awolowo University, University of Agriculture, Abeokuta

Abstract: 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 Yacubovich through the frequency domain technique.

Keywords: Periodic solutions, almost periodic solutions, bounded solutions, exponential stability, frequency domain.

Classification (MSC2000): 34C11; 34C25, 34D20

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