Oscillation of three-dimensional time scale systems with fixed point theorems

Oscillation and nonoscillation theories play very important roles in gaining information about the long-time behavior of solutions of a system. Therefore, we investigate the asymptotic behavior of nonoscillatory solutions as well as the existence of such solutions so that one can determine the limit behavior. For the existence, we use some fixed point theorems such as Schauder?s fixed point theorem and the Knaster fixed point theorem.

Nonlinear Second Order Impulsive Difference Equations and their Oscillation Properties

In this work, we state and discuss the sufficient conditions for oscillation and nonoscillation of a class of nonlinear second order neutral impulsive difference equations with fixed moments of impulsive effect for various ranges of the neutral coefficient p(n).

Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.