Oscillation of Nonlinear Neutral Delay Difference Equations of Fourth Order

Ramasamy Vimala, Ramasamy Kodeeswaran, Robert Cep (), Majella Jenvi Ignatia Krishnasamy, Meenakshi Awasthi and Govindasamy Santhakumar
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Ramasamy Vimala: Department of Mathematics, Kandaswami Kandar’s College, Velur 638182, India
Ramasamy Kodeeswaran: Department of Mathematics, Kandaswami Kandar’s College, Velur 638182, India
Robert Cep: Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic
Majella Jenvi Ignatia Krishnasamy: Department of Mathematics, SIMATS School of Engineering, Thandalam 602105, India
Meenakshi Awasthi: Department of Electronics and Communication Engineering, Ajay Kumar Garg Engineering College, Ghaziabad 201009, India
Govindasamy Santhakumar: Department of Electronics and Communication Engineering, Sri Krishna College of Technology, Coimbatore 641042, India

Mathematics, 2023, vol. 11, issue 6, 1-13

Abstract: This paper focuses on the study of the oscillatory behavior of fourth-order nonlinear neutral delay difference equations. The authors use mathematical techniques, such as the Riccati substitution and comparison technique, to explore the regularity and existence properties of the solutions to these equations. The authors present a new form of the equation: Δ ( a ( m ) ( Δ 3 z ( m ) ) p 1 − 1 ) + p ( m ) w p 2 − 1 ( σ ( m ) ) = 0 , where z ( m ) = w ( m ) + q ( m ) w ( m − τ ) with the following conditions: ∑ s = m 0 ∞ 1 a ( 1 p 1 − 1 ( s ) ) = ∞ . The equation represents a system where the state of the system at any given time depends on its current time and past values. The authors demonstrate new insights into the oscillatory behavior of these equations and the conditions required for the solutions to be well-behaved. They also provide a numerical example to support their findings.

Keywords: modified oscillation; fourth order; delay; neutral difference equation; nonlinear; Riccati transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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