New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

Abstract

The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.

Oscillatory Properties of Third-order Neutral Delay Difference Equations

“…and established some criteria for the oscillation of certain third-order DEs using comparison principles with a suitable couple of first order DEs. For more about the related works the authors are refer [10][11][12][13][14][15][16][17] to the readers.…”

Application of Fourier Transform to Study Hyers-Ulam Stability of Linear Differential Equations

“…where a is a four times continuously differentiable function, h, f, u and g are scalars and ξ(e) is the continuously differentiable function. There are many related works [12][13][14][15][16][17][18][19] and the reference references cited therein. The outline of the paper as follows: In Section 2, some definitions are introduced.…”

Asymptotic Behavior of Solutions of Third-order Non-linear Neutral Difference Equations

“…Without loss of oversimplification, we manage ultimately positive solutions of (1.1) since, under our suspicions on β, in case z(i) is an solution of condition (1.1), so is −z(i). For more about the related works the authors are refer [11][12][13][14][15][16][17][18] to the readers.…”