scholarly journals A THEOREM ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR ABSTRACT, QUASI-LINEAR DIFFERENTIAL EQUATIONS

1980 ◽  
Vol 13 (4) ◽  
pp. 787-808
Author(s):  
Ryszard Bittner ◽  
Zygfryd Smentek
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Linear Differential Equations ◽  
Uniqueness Of Solutions ◽  
Linear Differential

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.

scholarly journals An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1183
Author(s):  
Adrian Nicolae Branga ◽  
Ion Marian Olaru
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Linear Differential Equations ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Linear Differential

In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.

scholarly journals Existence and uniqueness of solutions for the first-order non-linear differential equations with three-point boundary conditions

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1387-1395
Author(s):  
Misir Mardanov ◽  
Yagub Sharifov ◽  
Kamala Ismayilova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contraction Mapping Principle ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear System

In this paper the existence and uniqueness of the solutions to boundary value problems for the first order non-linear system of the ordinary differential equations with three-point boundary conditions are investigated. For the first time the Green function is constructed and the considered problem is reduced to the equivalent integral equations that allow us to prove the existence and uniqueness theorems in differ from existing works, applying the Banach contraction mapping principle and Schaefer?s fixed point theorem. An example is given to illustrate the obtained results.

scholarly journals Existence and Uniqueness of Solutions for the First Order Non-linear Differential Equations with Multi-point Boundary Conditions

2020 ◽  
Vol 13 (3) ◽  
pp. 414-426
Author(s):  
M.J. Mardanov ◽  
Y.A. Sharifov ◽  
Humbet Aliyev Aliyev ◽  
R.A. Sardarova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Non Linear ◽  
Uniqueness Of The Solution ◽  
Linear Differential ◽  
The Green Function

This article discusses the existence and uniqueness of solutions for the system of non-linear first order ordinary differential equations with multipoint boundary conditions. The Green function is constructed, and the problem is reduced to the equivalent integral equation. Existence and uniqueness of the solution to this problem is studied using the Banach contraction mapping principle and Schaefer’s fixed point theorem.

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