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.

On application of the i-smooth analysis methodology to elaboration of numerical methods for solving functional differential equations

2021 ◽  
pp. 26-34
Author(s):  
Arkadii V. Kim
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Order Of Convergence ◽  
Functional Differential Equations ◽  
Convergence Conditions ◽  
Neutral Differential Equations ◽  
Infinite Dimensional ◽  
Analysis Methodology ◽  
Different Types ◽  
Functional Differential

The article discusses a number of aspects of the application of i -smooth analysis in the development of numerical methods for solving functional differential equations (FDE). The principle of separating finite- and infinite-dimensional components in the structure of numerical schemes for FDE is demonstrated with concrete examples, as well as the usage of different types of prehistory interpolation, those by Lagrange and Hermite. A general approach to constructing Runge–Kutta-like numerical methods for nonlinear neutral differential equations is presented. Convergence conditions are obtained and the order of convergence of such methods is established.

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.

scholarly journals Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 4
Author(s):  
Gennaro Infante
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Short Note ◽  
Type Theorem ◽  
Functional Differential Equations ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Growth Conditions ◽  
Functional Differential Systems ◽  
Functional Differential

Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of elliptic functional differential equations subject to functional boundary conditions. We obtain a localization of the corresponding non-negative eigenfunctions in terms of their norm. Under additional growth conditions, we also prove the existence of an unbounded set of eigenfunctions for these systems. The class of equations that we study is fairly general and our approach covers some systems of nonlocal elliptic differential equations subject to nonlocal boundary conditions. An example is presented to illustrate the theory.

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