Some Uniqueness Results for Impulsive Semilinear Neutral Functional Differential Equations

2002 ◽  
Vol 9 (3) ◽  
pp. 423-430
Author(s):  
M. Benchohra ◽  
A. Ouahabi
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Functional Differential ◽  
The Banach Contraction Principle

Abstract The Banach contraction principle is used to investigate the existence and uniqueness of solutions for first and second order impulsive semilinear neutral functional differential equations in Banach spaces.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN Lp(Ω, Ch)

2009 ◽  
Vol 09 (04) ◽  
pp. 597-612
Author(s):  
HAIBO BAO ◽  
DAQING JIANG
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we shall consider the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay in Lp(Ω, Ch) space: [Formula: see text] where we assume f : R+ × Lp(Ω, Ch) → Lp(Ω, Rn), g : R+ × Lp(Ω, Ch) → Lp(Ω, L(Rm, Rn)), p > 2, and B(t) is a given m-dimensional Brownian motion.

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