Abstract
This paper is concerned with oscillation and nonoscillation of a kind of nonlinear neutral impulsive differential systems with constant coefficients and constant delays by using the pulsatile constant. The sufficient and necessary conditions for oscillation in the case δ ∈ R\{0} are obtained. Two examples are included using the main results.
Highlights
Consider a class of first-order nonlinear neutral delay differential equations of the form (1)y(t) − δ y(t − τ) + β eγy(t−σ) − 1 = 0, where γ, τ > 0, σ ≥ 0 and β are real constants
This paper is concerned with oscillation and nonoscillation of a kind of nonlinear neutral impulsive differential systems with constant coefficients and constant delays by using the pulsatile constant
The main aim of this work is to study oscillation and nonoscillation properties governing the impulse operators acting on (1) which we denote as the impulsive systems y(t) − δ y(t − τ)
Summary
Consider a class of first-order nonlinear neutral delay differential equations of the form (1). In the present years much effort has been devoted to study the oscillatory and asymptotic behaviour of solutions of various classes of functional differential equations of neutral type (see for e.g [16], [17]). The author have made an attempt to study the oscillation and nonoscillation properties of solutions of a class of nonlinear neutral first order impulsive differential systems of the form (E). ∆ y(τk) + δ (τk)y(τk − τ) + α(τk)G y(τk − σ ) = 0, k ∈ N and established sufficient and necessary conditions for oscillation of all solutions of (E1) for different ranges of δ (t) In this direction, we refer to the reader some of the related works [9]-[13]. A regular nontrivial solution y(t) of (E) is said to be nonoscillatory, if there exists a point t0 ≥ 0 such that y(t) has a constant sign for t ≥ t0; otherwise, the regular solution y(t) is said to be oscillatory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
