Abstract
This work is concerned with the oscillatory behavior of solutions of fourth-order neutral differential equations. By using the Riccati transformation and integral averaging techniques we obtain some new Kamenev-type and Philos-type oscillation criteria. Our results extend and improve some known results in the literature. An example is given to illustrate our main results.
Highlights
In this paper, we establish some oscillation criteria for the fourth-order neutral differential equation of the formLy + q(t)yβ δ(t) = 0, t ≥ t0, (1)where Ly = r(t)(z (t))γ and z(t) := y(t) + p(t)y(τ (t))
The authors in [28, 29] were concerned with oscillatory behavior of solutions of fourth-order neutral differential equations and established some new oscillation criteria
6 Conclusions The aim of this paper was to provide a study of asymptotic nature for a class of fourthorder neutral delay differential equations
Summary
We establish some oscillation criteria for the fourth-order neutral differential equation of the form. The authors in [28, 29] were concerned with oscillatory behavior of solutions of fourth-order neutral differential equations and established some new oscillation criteria. Our aim in the present paper is employing the Riccati technique to establish some new Kamenev-type and Philos-type conditions for the oscillation of all solutions of equation (1) under condition (2). 3, we establish new oscillation results for (1) by using Riccati transformation. 4, we establish some new Kamenev-type oscillation criteria for (1). 5, we use the integral averaging technique to establish some new Philos-type conditions for the oscillation of all solutions of equation (1). Remark 1.1 All functional inequalities considered in this paper are assumed to hold eventually, that is, they are satisfied for all t large enough.
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