Electron. J. Diff. Eqns., Vol. 2004(2004), No. 59, pp. 130.
Damped second order linear differential equation with
deviating arguments: Sharp results in oscillation properties
Leonid Berezansky & Yury Domshlak
Abstract:
This article presents a new approach for investigating the oscillation
properties of second order linear differential equations with a damped term
containing a deviating argument
To study this equation, a specially adapted version of Sturmian Comparison
Method is developed and the following results are obtained:
(a) A comprehensive description of all critical (threshold) states
with respect to its oscillation properties
for a linear autonomous delay differential equation
(b) Two versions of SturmLike Comparison Theorems.
Based on these Theorems, sharp conditions under which all solutions are
oscillatory for specific realizations of
and
are obtained.
These conditions are formulated as the unimprovable analogues of the classical
Knezer Theorem which is wellknown for ordinary differential equations
(,
).
(c) Upper bounds for intervals, where
any solution has at least one zero.
Submitted March 23, 2004. Published April 19, 2004.
Math Subject Classifications: 34K11
Key Words: Linear differential equation with deviating arguments,
second order, damping term, oscillation, Sturmian comparison method
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Leonid Berezansky
Department of Mathematics
BenGurion University of the Negev
BeerSheva 84105, Israel
email: brznsky@cs.bgu.ac.il 

Yury Domshlak
Department of Mathematics
BenGurion University of the Negev
BeerSheva 84105, Israel
email: domshlak@cs.bgu.ac.il 
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