First-order impulsive differential systems: sufficient and necessary conditions for oscillatory or asymptotic behavior

Abstract

In this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results.

On the Monotonic and Asymptotic Properties of Positive Solutions to Third-Order Neutral Differential Equations and Their Effect on Oscillation Criteria

“…The study of the oscillatory behavior of differential equations has received great and continuous attention from researchers. Philos [14] and Santra et al [15,16] were interested in first-order differential equations. While, the works in [17][18][19][20][21][22] were concerned with even-and odd-order differential equations, with their various classifications.…”

Sawi transform and Hyers-Ulam stability of n t h order linear differential equations

“…Singh [29] tackled the popular issue of development by fostering its numerical model as far as first order linear DE using ST. Gupta [3] introduced connection among Sawi and other essential transforms. The applications of differential equations in various fields, for example, the environment, financial matters, science and engineering can be displayed as [25][26][27][28][29][30][31][32]. Recently Viglialoro [10,15,30] investigated the properties of solutions to porous medium problems with different sources and boundary conditions, boundedness in a chemotaxis system with consumed chemoattractant and bounded solutions to a parabolic-elliptic chemotaxis system with nonlinear diffusion and signal-dependent sensitivity.…”

On Nonlinear Forced Impulsive Differential Equations under Canonical and Non-Canonical Conditions

“…For further details on neutral IDS, we refer the reader to the papers [22][23][24][25][26][27][28][29][30][31][32][33][34][35] and to the references therein.…”