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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