Existence and Uniqueness of Solutions of First-Order Differential Equations

1997 ◽  
pp. 119-154
Author(s):  
Alfred Gray ◽  
Michael Mezzino ◽  
Mark A. Pinsky
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
First Order Differential Equations

scholarly journals Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yameng Wang ◽  
Juan Zhang ◽  
Yufeng Sun
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Lower And Upper Solutions ◽  
Quasilinearization Method ◽  
Rapid Convergence ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Convergence Of Approximate Solutions

In this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establishing some new comparison principles, the results of the existence and uniqueness of solutions of the problem are given. Finally, we obtain the uniform and rapid convergence of the iterative sequences of approximate solutions via the coupled lower and upper solutions and quasilinearization method. In addition, an example is given to illustrate the feasibility of the method.

scholarly journals Existence and uniqueness of solutions for the system ofintegro-differential equations with three-point and nonlinear integral boundary conditions

2020 ◽  
Vol 99 (3) ◽  
pp. 23-37
Author(s):  
M.J. Mardanov ◽  
◽  
Y.A. Sharifov ◽  
K.E. Ismayilova ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
First Order ◽  
Fixed Point Principle ◽  
Uniqueness Of A Solution

The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the boundary value problems for the first order nonlinear system of integro- differential equations with three-point and nonlinear integral boundary conditions are proved. A proof of uniqueness theorem of the solution is obtained by Banach fixed point principle, and the existence theorem then follows from Schaefer’s theorem.

scholarly journals Generalized two point boundary value problems. existence and uniqueness

1992 ◽  
Vol 5 (2) ◽  
pp. 147-156
Author(s):  
K. N. Murty ◽  
S. Sivasundaram
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Pseudo Inverse

An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document