Abstract
In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.
Highlights
This work is concerned with studying the oscillatory behavior of the higher-order neutral differential equation
We restrict our discussion to those solutions x of (1) which satisfy sup {|x (ς)| : ς1 ≤ ς0 } > 0 for every ς1 ∈ [ς x, ∞) and tacitly assume that (1)
The study of the problem of oscillation of differential equations with higher order has attracted the attention of many researchers in recent times
Summary
This work is concerned with studying the oscillatory behavior of the higher-order neutral differential equation Τ (ς) ≤ ς, limς→∞ τ (ς) = ∞ and there exists a nonnegative function h such that f (ς, x) ≥ h (ς) xβ, β is a ratio of odd positive The equation itself is termed oscillatory if all its solutions oscillate.
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.
