New Results for Oscillatory Behavior of Fourth-Order Differential Equations

Authors :: Omar Bazighifan
Osama Moaaz
Rami Ahmad El-Nabulsi
Source :: Symmetry, Volume 12, Issue 1, Symmetry, Vol 12, Iss 1, p 136 (2020)
Publication Year :: 2020
Publisher :: Multidisciplinary Digital Publishing Institute, 2020.
Abstract: Our aim in the present paper is to employ the Riccatti transformation which differs from those reported in some literature and comparison principles with the second-order differential equations, to establish some new conditions for the oscillation of all solutions of fourth-order differential equations. Moreover, we establish some new criterion for oscillation by using an integral averages condition of Philos-type, also Hille and Nehari-type. Some examples are provided to illustrate the main results.