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An Oscillation Criterion for First Order Linear Delay Differential Equations

Published online by Cambridge University Press:  20 November 2018

CH. G. Philos  and
Y. G. Sficas
CH. G. Philos
Affiliation:
Department of Mathematics University of Ioannina P.O. Box 1186 451 10 Ioannina Greece
Y. G. Sficas
Affiliation:
Department of Mathematics University of Ioannina P.O. Box 1186 451 10 Ioannina Greece
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Abstract

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A new oscillation criterion is given for the delay differential equation ${x}'\,(t)\,+\,p(t)x\,(t\,-\,\text{ }\!\!\tau\!\!\text{ (t)})\,=\,0$ , where $p,\,\text{ }\!\!\tau\!\!\text{ }\,\in \,\text{C}\,\text{( }\!\![\!\!\text{ 0,}\,\infty ),\,\text{ }\!\![\!\!\text{ 0,}\,\infty )\text{)}$ and the function $T$ defined by $T(t)\,=\,t-\,\text{ }\!\!\tau\!\!\text{ }\,\text{(t),}\,\text{t}\ge \,\text{0}$ is increasing and such that ${{\lim }_{t\to \infty }}\,T(t)\,=\,\infty $ . This criterion concerns the case where $\lim \,{{\inf }_{t\to \infty }}\int _{T(t)}^{t}p(s)ds\le \frac{1}{e}$ .

Keywords

34K15Delay differential equationoscillation

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 2 , 01 June 1998 , pp. 207 - 213
Copyright
Copyright © Canadian Mathematical Society 1998

References

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