Oscillation of $2^{nd}$-Order Nonlinear Noncanonical Difference Equations with Deviating Argument (Journal of Nonlinear Modeling and Analysis, 2024)
The purpose of this paper is to establish some new criteria for theoscillation of the second-order nonlinear noncanonical difference equations ofthe form $$∆ (a (n) ∆x (n)) + q(n)x^β(g(n)) = 0, n ≥ n_0$$ under the assumption $$\sum\limits^∞_{s=n} \frac{1}{a(s)}< ∞.$$ Corresponding difference equations of both retarded and advanced type arestudied. A particular example of Euler type equation is provided in order toillustrate the significance of our main results.
Keywords: Nonlinear difference equation; Retarded; Advanced; Noncanonical; Oscillation.