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Oscillation and Global Attractivity in a Periodic Delay Equation

Published online by Cambridge University Press:  20 November 2018

J. R. Graef ,
C. Qian  and
P. W. Spikes
J. R. Graef
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762, U.S.A.
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Abstract

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Consider the delay differential equation

where α(t) and β(t) are positive, periodic, and continuous functions with period w > 0, and m is a nonnegative integer. We show that this equation has a positive periodic solution x*(t) with period w. We also establish a necessary and sufficient condition for every solution of the equation to oscillate about x*(t) and a sufficient condition for x*(t) to be a global attractor of all solutions of the equation.

Keywords

34K2092D25oscillationglobal attractivityperiodic solutiondelay differential equation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 275 - 283
Copyright
Copyright © Canadian Mathematical Society 1996

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