Oscillation of $2^{nd}$-Order Nonlinear Noncanonical Difference Equations with Deviating Argument

Abstract

The purpose of this paper is to establish some new criteria for the oscillation of the second-order nonlinear noncanonical difference equations of the 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 are studied. A particular example of Euler type equation is provided in order to illustrate the significance of our main results.