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ON THE BEHAVIOUR OF THE OSCILLATORY SOLUTIONS OF SECOND-ORDER LINEAR UNSTABLE TYPE DELAY DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  23 May 2005

Ch. G. Philos ,
I. K. Purnaras  and
Y. G. Sficas
Ch. G. Philos
Affiliation:
Department of Mathematics, University of Ioannina, PO Box 1186, 451 10 Ioannina, Greece (cphilos@cc.uoi.gr; ipurnara@cc.uoi.gr; ysficas@cc.uoi.gr)
I. K. Purnaras
Affiliation:
Department of Mathematics, University of Ioannina, PO Box 1186, 451 10 Ioannina, Greece (cphilos@cc.uoi.gr; ipurnara@cc.uoi.gr; ysficas@cc.uoi.gr)
Y. G. Sficas
Affiliation:
Department of Mathematics, University of Ioannina, PO Box 1186, 451 10 Ioannina, Greece (cphilos@cc.uoi.gr; ipurnara@cc.uoi.gr; ysficas@cc.uoi.gr)
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Abstract

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Second-order linear (non-autonomous as well as autonomous) delay differential equations of unstable type are considered. In the non-autonomous case, sufficient conditions are given in order that all oscillatory solutions are bounded or all oscillatory solutions tend to zero at $\infty$. In the case where the equations are autonomous, necessary and sufficient conditions are established for all oscillatory solutions to be bounded or all oscillatory solutions to tend to zero at $\infty$.

Keywords

Primary 34K1134K1234K2034K25delay differential equationoscillatory solutionsbehaviour of oscillatory solutionsboundednessasymptotic decay
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 2 , June 2005 , pp. 485 - 498
Copyright
Copyright © Edinburgh Mathematical Society 2005