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Oscillation of Noncanonical Nonlinear Second-Order Neutral Difference Equations via One Condition

Year: 2026

Type: article

Abstract: This paper investigates the oscillation properties of solutions to a second-order nonlinear difference equation in noncanonical form with bounded and unbounded neutral terms. By employing the monotonicity of the neutral term together with a linearization technique, we establish new conditions that guarantee all solutions of the equation oscillate. Our results are applicable to various nonlinear forms of the equation, and, notably, the oscillation of all solutions is ensured through a single condition. Consequently, the proposed oscillation criteria are straightforward to apply and distinct from existing results on nonlinear difference equations. Four examples are presented to demonstrate the novelty and significance of the main findings.

Source: Mathematics

DOI: 10.3390/math14101735

Authors: Natarajan Prabaharan, Kumar S. Vidhyaa, George E. Chatzarakis, Ethiraju Thandapani

Institutions: R.M.D. Engineering College, Easwari Engineering College, School of Pedagogical and Technological Education, University of Madras

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W7161541758

FWCI:

Cites: 15

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