Oscillatory and Property Conditions for Third Order Difference Equation with Negative Middle-Term

Abstract

This paper presents a detailed analysis of the oscillation and Property A conditions for third-order advanced difference equations with negative middle terms. The authors employ the generalized Riccati transformation technique and summation by parts to establish sufficient criteria for the solutions to be oscillatory or have Property A. The main results and their proofs are presented clearly and concisely. The difference equations have been a topic of interest in various scientific fields such as economics, physics, and mathematical biology. The results presented in this paper can be used to inform the development of more accurate models for real-world problems in various scientific fields. Additionally, this paper explores the economic theory of business cycles and its mathematical foundations, specifically Samuelson's model, which outlines five potential trajectories or trends that economic activity can follow based on different combinations of the marginal propensity to consume multiplier parameter(α) and the accelerator coefficient (β).