University of Cambridge Numerical Analysis Reports Existence, Uniqueness and Continuous Dependence for Neutral Equations with State-dependent Delays Existence, Uniqueness and Continuous Dependence for Neutral Equations with State-dependent Delays
نویسنده
چکیده
The purpose of this work is to consider an initial value problem for neutral functional diierential equations with state dependent and vanishing delays. A gener-alised version of Schauder's xed point theorem which is based on the ball measure of noncompactness is used to obtain local existence of solutions and a comparison theorem. Results on continuation, uniqueness and continuous dependence of solutions are presented. The necessity of some critical assumptions made on certain Lipschitz constants is discussed.
منابع مشابه
Existence and continuous dependence for fractional neutral functional differential equations
In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.
متن کاملOn time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays
In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory
متن کاملExistence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay
...
متن کاملA note on existence and uniqueness of solutions of neutral functional-differential equations with state-dependent delays
Existence and uniqueness theorem for state-dependent delay-differential equations of neutral type is given. This theorem generalizes previous results by Grimm and the author.
متن کاملExistence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existe...
متن کامل