Oscillation criteria for third-order delay differential equations

By George E. Chatzarakis, Said R. Grace, Irena Jadlovská. Advances in Differential Equations, 2017

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The objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of a linear third-order delay differential equation of the form (r2(t)(r1(t)y′(t))′)′+q(t)y(τ(t))=0.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bigl( r_{2}(t) \bigl( r_{1}(t)y'(t) \bigr) ' \bigr) '+q(t)y \bigl(\tau(t) \bigr)= 0. $$\end{document} We establish new oscillation criteria that can be used to test for oscillations, even when the previously known criteria fail to apply. Examples illustrating the results are also given.

Subfields: Applied Mathematics, Numerical Analysis

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