Oscillation of Nonlinear Neutral Delay Difference Equations of Fourth Order
Ramasamy Vimala,
Ramasamy Kodeeswaran,
Robert Cep,
Majella Jenvi Ignatia Krishnasamy,
Meenakshi Awasthi,
Govindasamy Santhakumar
Affiliations
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
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)(Δ3z(m))p1−1)+p(m)wp2−1(σ(m))=0, where z(m)=w(m)+q(m)w(m−τ) with the following conditions: ∑s=m0∞1a(1p1−1(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.
