On oscillatory first order nonlinear neutral differential equations with nonlinear impulses

Santra, Shyam Sundar; Tripathy, Arun Kumar

doi:10.1007/s12190-018-1178-8

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Cited by 18 publications

(10 citation statements)

References 12 publications

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“…In their work, 14 Santra and Tripathy investigated the oscillatory behavior of the solutions for first-order impulsive neutral delay differential equations of the form…”

Section: Respectively)mentioning

confidence: 99%

Second‐order impulsive differential systems with mixed delays: Oscillation theorems

Santra

Ghosh

Dassios

2021

Math Methods in App Sciences

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“…In their work, 14 Santra and Tripathy investigated the oscillatory behavior of the solutions for first-order impulsive neutral delay differential equations of the form…”

Section: Respectively)mentioning

confidence: 99%

Second‐order impulsive differential systems with mixed delays: Oscillation theorems

Santra

Ghosh

Dassios

2021

Math Methods in App Sciences

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show abstract

“…In [14], Santra and Tripathy investigated the oscillatory behaviour of the solutions for first-order impulsive neutral delay differential equations of the form…”

Section: Introductionmentioning

confidence: 99%

“…Suppose (a)-(f ) hold for ι ≥ ι 0 , and u is an eventually positive solution of (10)-(11). Then w satisfies u(ι) ≥ (1a)w(ι) for ι ≥ ι 1 (14). …”

mentioning

confidence: 99%

Second-order impulsive differential systems with mixed and several delays

et al. 2021

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In this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

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“…In [16], Santra and Tripathy investigated the oscillatory or asymptotic behavior of the solutions for first-order neutral delay differential system…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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On oscillatory first order nonlinear neutral differential equations with nonlinear impulses

Cited by 18 publications

References 12 publications

Second‐order impulsive differential systems with mixed delays: Oscillation theorems

Second‐order impulsive differential systems with mixed delays: Oscillation theorems

Second-order impulsive differential systems with mixed and several delays

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

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