Neutral Differential Equations of Second-Order: Iterative Monotonic Properties

Osama Moaaz, Fahd Masood, Clemente Cesarano, Shami A. M. Alsallami, E. M. Khalil and Mohamed L. Bouazizi
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Osama Moaaz: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Fahd Masood: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Clemente Cesarano: Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy
Shami A. M. Alsallami: Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
E. M. Khalil: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Mohamed L. Bouazizi: Department of Mechanical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Alkharj 16273, Saudi Arabia

Mathematics, 2022, vol. 10, issue 9, 1-11

Abstract: In this work, we investigate the oscillatory properties of the neutral differential equation ( r ( l ) [ ( s ( l ) + p ( l ) s ( g ( l ) ) ) ′ ] v ) ′ + ∑ i = 1 n q i ( l ) s v ( h i ( l ) ) = 0 , where s ≥ s 0 . We first present new monotonic properties for the solutions of this equation, and these properties are characterized by an iterative nature. Using these new properties, we obtain new oscillation conditions that guarantee that all solutions are oscillate. Our results are a complement and extension to the relevant results in the literature. We test the significance of the results by applying them to special cases of the studied equation.

Keywords: Emden–Fowler; neutral differential equations; oscillation; non-canonical (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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