Electron. J. Diff. Equ., Vol. 2012 (2012), No. 97, pp. 1-11.

Existence and nonexistence of periodic solutions of n-vector differential equations of orders six and seven

Victor F. Payne, Haroon Oladipo Tejumola

Abstract:
In this article, we extend our earlier results and establish new ones on the existence and non-existence of periodic solutions for n-vector non-dissipative, nonlinear ordinary differential equations. Our results involve both the homogeneous and non-homogeneous cases. The setting for non-existence results of periodic solutions involves a suitably defined scalar function endowed with appropriate properties relative to each equation. But the framework for proving existence results is via the standard Leray-Schauder fixed-point technique whose central theme is the verification of a-priori bounded periodic solutions for a parameter-dependent system of equations.

Submitted April 12, 2012. Published June 10, 2012.
Math Subject Classifications: 34C25, 34K05, 34K13.
Key Words: A priori bound; Leray-Schauder fixed-point teorem; parameter-dependent system; periodic solution.

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Victor F. Payne
Department of Mathematics, University of Ibadan
Ibadan Nigeria
email: vpayne34@gmail.com
Haroon Oladipo Tejumola
Department of Mathematical Sciences
Redeemer's University
Mowe, Ogun State, Nigeria
email: haroontej@yahoo.co.uk

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