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Stability of the second order delay differential equations with a damping term

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Abstract

For the delay differential equations

$$ \ddot x(t) + a(t)\dot x(g(t)) + b(t)x(h(t)) = 0,g(t) \leqslant t,h(t) \leqslant t, $$

and

$$ \ddot x(t) + a(t)\dot x(t) + b(t)x(t) + a_1 (t)\dot x(g(t)) + b_1 (t)x(h(t)) = 0 $$

explicit exponential stability conditions are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel

    Leonid Berezansky

  2. Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB, T2N1N4, Canada

    Elena Braverman

  3. Department of Mathematics and Computer Science, Ariel University Center, Ariel, 44837, Israel

    Alexander Domoshnitsky

Authors
  1. Leonid Berezansky
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  2. Elena Braverman
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  3. Alexander Domoshnitsky
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Correspondence to Leonid Berezansky.

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Berezansky, L., Braverman, E. & Domoshnitsky, A. Stability of the second order delay differential equations with a damping term. Differ Equ Dyn Syst 16, 185–205 (2008). https://doi.org/10.1007/s12591-008-0012-4

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  • DOI: https://doi.org/10.1007/s12591-008-0012-4

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