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

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.