Abstract
In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations.
Highlights
This paper deals with the oscillatory behavior of solutions to a third-order linear neutral delay differential equation of the form r2 (t) r1 (t)y0 (t)
Mathematics 2019, 7, 1177 and assume without further mention that L3 y is of noncanonical type, that is, Z ∞
Our contribution should be of interest to the reader as, contrary to the majority of results in the literature, we attain the oscillation of all solutions of (1), and find the conditions of all theorems very simple and easy to verify
Summary
This paper deals with the oscillatory behavior of solutions to a third-order linear neutral delay differential equation of the form r2 (t) r1 (t)y0 (t) Under a solution of Equation (1), we mean a nontrivial function x ∈ C 1 ([Ty , ∞), R) with Ty ≥ t0 , which has the property Li y ∈ C 1 ([Ty , ∞), R), i = 0, 1, 2, and satisfies (1) on [Ty , ∞). The equation itself is termed oscillatory if all its solutions oscillate.
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