Abstract
In this article, we prove some new oscillation theorems for fourth-order differential equations. New oscillation results are established that complement related contributions to the subject. We use the Riccati technique and the integral averaging technique to prove our results. As proof of the effectiveness of the new criteria, we offer more than one practical example.
Highlights
Equation (1) into a first-order equation, while in our article, we discuss the oscillatory properties of differential equations with a middle term and with a canonical operator of the neutral-type, and we employ a different approach based on using the integral averaging technique and the Riccati technique to reduce the main equation into a first-order inequality to obtain more effective oscillatory properties
We prove some new oscillation theorems for (1)
New oscillation results are established that complement related contributions to the subject
Summary
We are concerned with the asymptotic behavior of solutions to fourth-order differential equations: m(z)Ψr1 ς000 (z). The theory of the oscillation of delay of differential equations is a fertile study area and has attracted the attention of many authors recently. Chatzarakis et al [9], by using the Riccati technique, established asymptotic behavior for the following neutral equation: m(z) ς000 (z). The authors in [6,7] used the comparison technique that differs from the one we used in this article Their approach is based on using these mentioned methods to reduce. Equation (1) into a first-order equation, while in our article, we discuss the oscillatory properties of differential equations with a middle term and with a canonical operator of the neutral-type, and we employ a different approach based on using the integral averaging technique and the Riccati technique to reduce the main equation into a first-order inequality to obtain more effective oscillatory properties. The authors in [6,7] used a comparison technique that differs from the one we used in this article
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