Nonlinear differential equations of fourth-order: Qualitative properties of the solutions

• Main Author: Omar Bazighifan
• Format: Article
• Language: English
• Published: AIMS Press 2020-08-01
• Series: AIMS Mathematics
• Subjects: fourth-order differential equations; neutral delay; oscillation
• Online Access: https://www.aimspress.com/article/10.3934/math.2020414/fulltext.html

In this paper, we study the oscillation of solutions for a fourth-order neutral nonlinear differential equation, driven by a $p$-Laplace differential operator of the form \begin{equation*} \begin{cases} \left( r\left( t\right) \Phi _{p_{1}}[w^{\prime \prime \prime }\left( t\right) ]\right) ^{\prime }+q\left( t\right) \Phi _{p_{2}}\left( u\left( \vartheta \left( t\right) \right) \right) =0, & \\ r\left( t\right) >0,\ r^{\prime }\left( t\right) \geq 0,\ t\geq t_{0}>0, & \end{cases} \end{equation*} The oscillation criteria for these equations have been obtained. Furthermore, some examples are given to illustrate the criteria.