W-transform for exponential stability of second order delay differential equations without damping terms

Alexander Domoshnitsky; Abraham Maghakyan; Leonid Berezansky

doi:10.1186/s13660-017-1296-0

W-transform for exponential stability of second order delay differential equations without damping terms

J Inequal Appl. 2017;2017(1):20. doi: 10.1186/s13660-017-1296-0. Epub 2017 Jan 17.

Authors

Alexander Domoshnitsky¹, Abraham Maghakyan¹, Leonid Berezansky²

Affiliations

¹ Department of Mathematics, Ariel University, Ariel, Israel.
² Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105 Israel.

Abstract

In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.

Keywords: W-method; exponential stability; second order delay differential equations.