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dc.contributor.authorBerezansky, Leonid ( Orcid Icon 0000-0001-5284-6137 )
dc.contributor.authorDomshlak, Yury ( )
dc.identifier.citationBerezansky, L., & Domshlak, Y. (2004). Damped second order linear differential equation with deviating arguments: Sharp results in oscillation properties. Electronic Journal of Differential Equations, 2004(59), pp. 1-30.en_US

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

x''(t) - [P(t)x(r(t))]' + Q(t)x(l(t)) = 0, r(t) ≤ t.

To study this equation, a specially adapted version of Sturmian Comparison Method is developed and the following results are obtained:

  1. A comprehensive description of all critical (threshold) states with respect to its oscillation properties for a linear autonomous delay differential equation
    y''(t) - py' (t - τ) + qy (t - σ) = 0, τ > 0, ∞ < σ < ∞.
  2. Two versions of Sturm-Like Comparison Theorems. Based on these Theorems, sharp conditions under which all solutions are oscillatory for specific realizations of P(t), r(t) and l(t) are obtained. These conditions are formulated as the unimprovable analogues of the classical Knezer Theorem which is well-known for ordinary differential equations (P(t) = 0, l(t) = t).
  3. Upper bounds for intervals, where any solution has at least one zero.
dc.format.extent30 pages
dc.format.medium1 file (.pdf)
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectLinear differential equation with deviating argumentsen_US
dc.subjectSecond orderen_US
dc.subjectDamping termen_US
dc.subjectSturmian comparison methoden_US
dc.titleDamped second order linear differential equation with deviating arguments: Sharp results in oscillation propertiesen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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