Abstract
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 \t\t\t(r2(t)(r1(t)y′(t))′)′+q(t)y(τ(t))=0.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\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.
Highlights
The equation itself is termed oscillatory if all of its solutions oscillate
We restrict our attention to those solutions of ( . ) which exist on I and satisfy the condition sup{|x(t)| : t ≥ t } > for any t ≥ ty
The iterative nature of the results enables us to test for oscillations, even when the previously known results fail to apply
Summary
The equation itself is termed oscillatory if all of its solutions oscillate. ), see [ , Lemma ], authors have used various techniques to present sufficient conditions guaranteeing that any solution of As an example of this property, we can consider the third-order differential equation y (t) + y(t – τ ) = , τ > , which is oscillatory if and only if τ e > (see [ , Theorem ]).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
