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Open AccessArticle

New Results for Oscillatory Behavior of Fourth-Order Differential Equations

by Rami Ahmad El-Nabulsi 1,*,†, Osama Moaaz 2,† and Omar Bazighifan 3,†
1
Athens Institute for Education and Research, Mathematics and Physics Divisions, 10671 Athens, Greece
2
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3
Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(1), 136; https://doi.org/10.3390/sym12010136
Received: 19 December 2019 / Revised: 6 January 2020 / Accepted: 7 January 2020 / Published: 9 January 2020
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. View Full-Text
Keywords: oscillatory solutions; nonoscillatory solutions; fourth-order; delay differential equations; Riccati transformation; comparison theorem oscillatory solutions; nonoscillatory solutions; fourth-order; delay differential equations; Riccati transformation; comparison theorem
MDPI and ACS Style

El-Nabulsi, R.A.; Moaaz, O.; Bazighifan, O. New Results for Oscillatory Behavior of Fourth-Order Differential Equations. Symmetry 2020, 12, 136.

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