Electron. J. Diff. Eqns., Vol. 2001(2001), No. 40, pp. 1-19.

First-order differential equations with several deviating arguments: Sturmian comparison method in oscillation theory: I

Leonid Berezansky \& Yury Domshlak

Abstract:
The Sturmian Comparison Method, elaborated previously by one of the authors, is developed and applied to differential equations with several deviating arguments. For two delays, we obtain oscillation criteria that are explicit and close to be necessary. We also present a comparison of our results with those known in the literature.

Submitted January 16, 2001. Published May 31, 2001.
Math Subject Classifications: 34K11.
Key Words: delay differential equations, several delays, oscillation, non-oscillation, Sturmian comparison method.

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Leonid Berezansky
Department of Mathematics
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel
e-mail: brznsky@cs.bgu.ac.il
Yury Domshlak
Department of Mathematics
Ben-Gurion University of the Negev
Beer-Sheva 84105, Israel
e-mail: domshlak@cs.bgu.ac.il

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