OSCILLATION THEOREMS FOR SECOND-ORDER NONLINEAR DIffERENCE EQUATIONS WITH NONLINEAR DAMPING TERMS: NEW CRITERIA AND APPLICATIONS

Abstract

This paper establishes new and improved oscillation criteria for second-order nonlinear difference equations with nonlinear damping terms. We develop novel sufficient conditions that generalize and enhance existing results in the literature by employing advanced Riccati transformation techniques and refined analytical methods. Our main contributions include the derivation of more general oscillation theorems that encompass broader classes of nonlinear functions and damping terms, along with the establishment of sharper conditions for oscillatory behavior. The theoretical results are supported by comprehensive examples that demonstrate the effectiveness and applicability of our criteria. Our findings significantly extend the current understanding of oscillatory dynamics in discrete nonlinear systems and provide valuable tools for analyzing complex difference equations arising in various scientific and engineering applications.