Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients

Abstract

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

Oscillation of the Solutions for Hematopoiesis Models

“…The wide attention in this article is motivated due to its important applications in some mathematical models that are used in ecology, biology, biomedical, and diffusion of some contagion diseases in human beings. For greater acquaintance with this study, the reader can see [1,2], because of its employment in our daily lives, the qualitative properties for oscillation of the hematopoiesis model have been appreciably investigated in the literature. In particular, a nonlinear model of Hematopoiesis stems from cell dynamics.…”

تذبذب نموذج تكون الدم النبضي مع معاملات موجبة وسالبة

“…Many authors looked for sufficient conditions to ensure oscillatory property for different differential equations. As a result, they established a lot of papers for oscillatory theory for ordinary [8][9][10][11] and delay differential equations [12][13][14][15] The oscillation criteria of various IDE, including super-half-linear IDE, halflinear impulsive differential equations, and mixed nonlinear differential equations, were obtained by researchers Ozbekler and Zafer, who published the impulsive differential equations as well 16 . The methodology for analyzing impulsive differential equations were supplied by Agarwal, Karakoc, and Zafer, who also offered a summary of various findings on the oscillation of IDE up to 2010 (see 7, Published Online First: December, 2023 https://dx.doi.org/10.21123/bsj.2023.8796 P-ISSN: 2078-8665 -E-ISSN: 2411-7986 Baghdad Science Journal ecological and biological dynamical systems.…”