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

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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