Existence and uniqueness of solutions of the first order nonlinear integro-differential equations with three-point boundary conditions

2018 ◽  
Author(s):  
Misir Mardanov ◽  
Yagub Sharifov ◽  
Farah Zeynalli
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order

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 results for the first-order non-linear impulsive integro-differential equations with two-point boundary conditions

2021 ◽  
Vol 102 (2) ◽  
pp. 74-83
Author(s):  
M.J. Mardanov ◽  
◽  
R.S. Mammadov ◽  
S.Yu. Gasimov ◽  
Ya.A. Sharifov ◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Contraction Mapping Principle ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Green Function

The article discusses the existence and uniqueness of solutions for a system of nonlinear integro-differential equations of the first order with two-point boundary conditions. The Green function is constructed, and the problem under consideration is reduced to equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach contraction mapping principle. Schaefer’s fixed point theorem is used to prove the existence of solutions.

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

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.

Unique Solution for Multi-point Fractional Integro-Differential Equations

2020 ◽  
Vol 21 (2) ◽  
pp. 219-226
Author(s):  
Chengbo Zhai ◽  
Lifang Wei
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Iterative Sequence ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractWe study a fractional integro-differential equation subject to multi-point boundary conditions: $$\left\{\begin{array}{l} D^\alpha_{0^+} u(t)+f(t,u(t),Tu(t),Su(t))=b,\ t\in(0,1),\\u(0)=u^\prime(0)=\cdots=u^{(n-2)}(0)=0,\\ D^p_{0^+}u(t)|_{t=1}=\sum\limits_{i=1}^m a_iD^q_{0^+}u(t)|_{t=\xi_i},\end{array}\right.$$where $\alpha\in (n-1,n],\ n\in \textbf{N},\ n\geq 3,\ a_i\geq 0,\ 0<\xi_1<\cdots<\xi_m\leq 1,\ p\in [1,n-2],\ q\in[0,p],b>0$. By utilizing a new fixed point theorem of increasing $\psi-(h,r)-$ concave operators defined on special sets in ordered spaces, we demonstrate existence and uniqueness of solutions for this problem. Besides, it is shown that an iterative sequence can be constructed to approximate the unique solution. Finally, the main result is illustrated with the aid of an example.

scholarly journals Stability analysis for first-order nonlinear differential equations with three-point boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
pp. 40-52
Author(s):  
Kamala E. Ismayilova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Fixed Point Principle ◽  
The Stability ◽  
The Given ◽  
Stability Results

AbstractIn the present paper, we study a system of nonlinear differential equations with three-point boundary conditions. The given original problem is reduced to the equivalent integral equations using Green function. Several theorems are proved concerning the existence and uniqueness of solutions to the boundary value problems for the first order nonlinear system of ordinary differential equations with three-point boundary conditions. The uniqueness theorem is proved by Banach fixed point principle, and the existence theorem is based on Schafer’s theorem. Then, we describe different types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability. We discuss the stability results providing suitable example.

scholarly journals Existence and Uniqueness of Solutions for the System of First-order Nonlinear Differential Equations with Three-point and Integral Boundary Conditions

2019 ◽  
Vol 12 (3) ◽  
pp. 756-770
Author(s):  
Misir Mardanov ◽  
Yagub Sharifov ◽  
Kamala Ismayilova ◽  
Sevinc Zamanova
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
First Order ◽  
The Green Function ◽  
The Given

In the paper, the existence and uniqueness of the solutions for the system of the nonlinear first-order ordinary differential equations with three-point and integral boundary conditions are studied. The Green function is constructed and the considered problem is reduced to the equivalent integral equation. The existence and uniqueness of the solutions for the given problem are analyzed by using the Banach contraction principle. The Schaefer’s fixed point theorem is thenused to prove the existence of the solutions. Finally, the examples are given to verify the given theorems.

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