Electron. J. Diff. Eqns., Vol. 2002(2002), No. 31, pp. 1-18.

Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II

Leonid Berezansky & Yury Domshlak

Abstract:
We study the oscillation of solutions to the differential equation
$$ \dot{x}(t) +a_1(t)x[r(t)]+a_2(t)x[p(t)]=0, \quad t\geq t_0 $$
which has a retarded argument $r(t)$ and an advanced argument $p(t)$. We obtain oscillation and non-oscillation conditions which are closed to be necessary. We provide examples to show that our results are best possible and compare them with known results.

Submitted November 29, 2001. Published April 1, 2002.
Math Subject Classifications: 34K11.
Key Words: mixed differential equations, 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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