scholarly journals An existence theory for functional-differential equations and functional-differential systems

1978 ◽  
Vol 29 (1) ◽  
pp. 86-104 ◽  
Author(s):  
E.K Ifantis
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Existence Theory ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential

scholarly journals Fully coupled forward–backward stochastic dynamics and functional differential systems

2015 ◽  
Vol 15 (02) ◽  
pp. 1550006
Author(s):  
Matteo Casserini ◽  
Gechun Liang
Keyword(s):  
Differential Equations ◽  
Stochastic Dynamics ◽  
Functional Differential Equations ◽  
Differential Systems ◽  
Time Direction ◽  
Functional Differential Systems ◽  
Classical Setting ◽  
Different Types ◽  
Functional Differential ◽  
Fully Coupled

This paper introduces and solves a general class of fully coupled forward–backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different types of forward–backward stochastic differential equations (FBSDEs) that do not fit in the classical setting. In our approach, the equations are running in the same time direction rather than in a forward and backward way, and the conflicting nature of the structure of FBSDEs is therefore avoided.

scholarly journals Solvability of discontinuous functional differential systems in l∞(M)

2006 ◽  
Vol 48 (2) ◽  
pp. 237-243
Author(s):  
A. Cabada ◽  
J. Ángel Cid ◽  
S. Heikkilä
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Infinite System ◽  
Functional Differential Equations ◽  
Extremal Solutions ◽  
Differential Systems ◽  
First Order ◽  
Functional Differential Systems ◽  
Bounded Functions ◽  
Functional Differential

AbstractWe study the existence of extremal solutions for an infinite system of first-order discontinuous functional differential equations in the Banach space of the bounded functions I∞(M).

scholarly journals On the Initial Value Problem for Functional Differential Systems

1994 ◽  
Vol 1 (4) ◽  
pp. 419-427
Author(s):  
V. Šeda ◽  
J. Eliaš
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Arbitrary Order ◽  
Functional Differential Equations ◽  
Infinite Interval ◽  
Initial Value ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential

Abstract For a system of functional differential equations of an arbitrary order the conditions are established for the initial value problem to be solvable on an infinite interval, and the structure of the set of solutions to this problem is studied.

Attractor minimal sets for non-autonomous delay functional differential equations with applications for neural networks

2005 ◽  
Vol 461 (2061) ◽  
pp. 2767-2783 ◽  
Author(s):  
Sylvia Novo ◽  
Rafael Obaya ◽  
Ana M Sanz
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Minimal Sets ◽  
Functional Differential Systems ◽  
Functional Differential

The dynamics of a class of non-autonomous, convex (or concave) and monotone delay functional differential systems is studied. In particular, we provide an attractivity result when two completely strongly ordered minimal subsets K 1 ≪ C K 2 exist. As an application of our results, sufficient conditions for the existence of global or partial attractors for non-autonomous delayed Hopfield-type neural networks are obtained.

scholarly journals On Asymptotic Behaviour of Solutions ton-Dimensional Systems of Neutral Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
H. Šamajová ◽  
E. Špániková
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Functional Differential Systems ◽  
Functional Differential

This paper presents the properties and behaviour of solutions to a class ofn-dimensional functional differential systems of neutral type. Sufficient conditions for solutions to be either oscillatory, orlimt→∞yi(t)= 0, orlimt→∞|yi(t)|=∞,i=1,2,…,n, are established. One example is given.

scholarly journals J-nonexpansive mappings in uniform spaces and applications

1991 ◽  
Vol 43 (2) ◽  
pp. 331-339 ◽  
Author(s):  
Vasil G. Angelov
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Functional Differential Equations ◽  
Uniform Convexity ◽  
Existence Theory ◽  
Uniform Spaces ◽  
Geometric Properties ◽  
Functional Differential

The purpose of the paper is to introduce a class of “j-nonexpansive” mappings and to prove fixed point theorems for such mappings. They naturally arise in the existence theory of functional differential equations. These mappings act in spaces without specific geometric properties as, for instance, uniform convexity. Critical examples are given.

Linear Functional-Differential Equations in a Banach Algebra*

1978 ◽  
Vol 21 (4) ◽  
pp. 435-439 ◽  
Author(s):  
W. J. Fitzpatrick ◽  
L. J. Grimm
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Banach Algebra ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Linear Functional ◽  
Banach Algebras ◽  
Functional Differential Equations ◽  
Differential Systems ◽  
Functional Differential

The theory of analytic differential systems in Banach algebras has been investigated by E. Hille and others, see for instance Chapter 6 in [4].In this paper we show how a projection method used by W. A. Harris, Jr., Y. Sibuya, and L. Weinberg [3] can be applied to study a class of functional differential equations in this setting. The method, based on functional analysis, had been used extensively by L. Cesari [1] in similar forms for boundary value problems, and by J. K. Hale, S. Bancroft, and D. Sweet [2]. We also obtain as corollaries several results for ordinary differential equations in Banach algebras which were proved in a different way by Hille.

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