On Existence and Uniqueness of Random Impulsive Differential Equations

Zhang, Shuorui

doi:10.1007/s11424-015-4018-z

Cited by 7 publications

(1 citation statement)

References 26 publications

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“…In [3], the authors proposed a random impulsive differential equations for k = 1, ..., m y ′ (r, t) = f (t, y(t, r), r), t ̸ = t k , y ′ (r, t + k ) − y ′ (r, t − k ) = I k (y(r, t k ), r), y(r, a) = ν(r), (3) here, the function ν ∈ C 0 (Ω → R n ) is a random variable. Under appropriate conditions in the parameters f , k, I, the existence and uniqueness is established owing to the generalized Schaefer's type random fixed-point theorem.…”

Section: Introduction and Position Of Problem 1results And Discussionmentioning

confidence: 99%

Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay

Moumen,

Ladrani,

Ferhat

et al. 2023

Fractal Fract

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In this paper, we consider a system of random impulsive differential equations with infinite delay. When utilizing the nonlinear variation of Leray–Schauder’s fixed-point principles together with a technique based on separable vector-valued metrics to establish sufficient conditions for the existence of solutions, under suitable assumptions on Y1, Y2 and ϖ1, ϖ2, which greatly enriched the existence literature on this system, there is, however, no hope to discuss the uniqueness result in a convex case. In the present study, we analyzed the influence of the impulsive and infinite delay on the solutions to our system. In addition, to the best of our acknowledge, there is no result concerning coupled random system in the presence of impulsive and infinite delay.

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Section: Introduction and Position Of Problem 1results And Discussionmentioning

confidence: 99%