An approach to the conditions for the existence and uniqueness of solutions of ordinary differential equations

1996 ◽  
Vol 80 (1) ◽  
pp. 1582-1596
Author(s):  
L. D. Kudryavtsev
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions

γ-product of white noise space and applications

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Samah Horrigue
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Ordinary Differential Equations ◽  
Existence And Uniqueness ◽  
Fock Space ◽  
Wick Product ◽  
Uniqueness Of Solutions ◽  
White Noise Space

AbstractIn this paper, we define and give some characteristic properties of γ-product in white noise space, which is the generalization of the Wick product. Existence and uniqueness of solutions are proved for a certain class of ordinary differential equations for the Fock space.

Stabilization of Functions and its Application

1994 ◽  
Vol 1 (2) ◽  
pp. 183-195
Author(s):  
L. D. Kudryavtsev
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fundamental System ◽  
Linear Differential Equations ◽  
Uniqueness Of Solutions ◽  
Strong Stabilization ◽  
Linear Differential ◽  
Polynomial Stabilization

Abstract The concepts of polynomial stabilization, strong polynomial stabilization, and strong stabilization are introduced for a fundamental system of solutions of linear differential equations. Some criteria of such kinds of stabilizations and applications to the theory of existence and uniqueness of solutions of ordinary differential equations are given. An abstract scheme of the obtained results is presented for Banach spaces.

Theory and applications of first-order systems of Stieltjes differential equations

2017 ◽  
Vol 6 (1) ◽  
pp. 13-36 ◽  
Author(s):  
Marlène Frigon ◽  
Rodrigo López Pouso
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Basic Theory ◽  
Dynamic Equations ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Set Up

AbstractWe set up the basic theory of existence and uniqueness of solutions for systems of differential equations with usual derivatives replaced by Stieltjes derivatives. This type of equations contains as particular cases dynamic equations on time scales and impulsive ordinary differential equations.

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