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Boundedness and Stability of Solutions to Certain Second Order Differential Equations


A. T. Ademola

Department of Mathematics,
Obafemi Awolowo University, Ile-Ife, Nigeria


In this paper the behaviour of solutions of certain second order nonlinear non-autonomous differential equations is considered. By employing the Lyapunov's second method, a suitable complete Lyapunov function is constructed and used to establish sufficient conditions that guarantee existence of solutions that are periodic, uniformly asymptotically stable and uniformly ultimately bounded. Obtained results are not only new but also include many outstanding recent results in the literature.

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