Abstract
The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.
Highlights
We study the oscillatory properties of solutions of the following fourthorder neutral differential equation
In future work we will study the oscillatory behavior of this equation by comparison method with second-order differential equations
Summary
We study the oscillatory properties of solutions of the following fourthorder neutral differential equation. The problems of oscillatory behavior of neutral differential equations have a number of practical applications in the study of distributed networks containing lossless transmission lines which arise in high-speed computers where the lossless transmission lines are used to interconnect switching circuits, see [1,2,3,4]. In [17], Bazighifan obtained oscillation conditions for solutions of (1) and used comparison method with second-order equations. Bazighifan and Abdeljawad [20] give some results providing information on the asymptotic behavior of solutions of fourth-order advanced differential equations. This time, the authors used comparison method with first and second-order equations.
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