On the oscillation of fourth-order delay differential equations

By Said R. Grace, Jozef Dzurina, Irena Jadlovská, Tongxing Li. Advances in Differential Equations, 2019

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In the paper, fourth-order delay differential equations of the form (r3(r2(r1y′)′)′)′(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}$$ \bigl(r_{3} \bigl(r_{2} \bigl(r_{1}y' \bigr)' \bigr)' \bigr)'(t) + q(t) y \bigl( \tau (t) \bigr) = 0 $$\end{document} under the assumption ∫t0∞dtri(t)<∞,i=1,2,3,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \int _{t_{0}}^{\infty }\frac{\mathrm {d}t}{r_{i}(t)} < \infty , \quad i = 1,2,3, $$\end{document} are investigated. Our newly proposed approach allows us to greatly reduce a number of conditions ensuring that all solutions of the studied equation oscillate. An example is also presented to test the strength and applicability of the results obtained.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8033d0fa1b21a4a0a80dfba1abda5dab9fffb0fb