MATHEMATICA BOHEMICA, Vol. 137, No. 3, pp. 355-364, 2012

Ultimate boundedness of some third order ordinary differential equations

Anthony Uyi Afuwape, M. O. Omeike

Anthony Afuwape, Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53-108, Medellín AA 1226, Colombia, e-mail: aafuwape@yahoo.co.uk; M. O. Omeike, Department of Mathematics, University of Agriculture, Abeokuta, Nigeria, e-mail: moomeike@yahoo.com

Abstract: We prove the ultimate boundedness of solutions of some third order nonlinear ordinary differential equations using the Lyapunov method. The results obtained generalize earlier results of Ezeilo, Tejumola, Reissig, Tunc and others. The Lyapunov function used does not involve the use of signum functions as used by others.

Keywords: ultimate boundedness, complete Lyapunov function, differential equation of third-order

Classification (MSC 2010): 34K20

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