scholarly journals Existence and uniqueness of iterative positive solutions for singular Hammerstein integral equations

2017 ◽  
Vol 10 (07) ◽  
pp. 3364-3380 ◽  
Author(s):  
Xinqiu Zhang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Integral Equations ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Hammerstein Integral Equations

Existence and uniqueness theorem for set-valued Volterra–Hammerstein integral equations

2018 ◽  
Vol 11 (03) ◽  
pp. 1850036 ◽  
Author(s):  
Andrej V. Plotnikov ◽  
Tatyana A. Komleva ◽  
Irina V. Molchanyuk
Keyword(s):  
Uniqueness Theorem ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Hammerstein Integral Equations

In this paper, we consider two types of set-valued Volterra–Hammerstein integral equations and prove the existence and uniqueness theorem.

scholarly journals A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. A. El-Ameen ◽  
M. El-Kady
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Integral Equations ◽  
Simple Form ◽  
Existence And Uniqueness ◽  
Direct Method ◽  
New Method ◽  
Fredholm Integral Equations ◽  
Hammerstein Integral Equations

A new method for solving nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.

scholarly journals A Sum Operator Method for the Existence and Uniqueness of Positive Solutions to a System of Nonlinear Fractional Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jing Wu ◽  
Tunhua Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Iterative Scheme ◽  
Operator Method ◽  
Quadratic System ◽  
System Of Integral Equations ◽  
Fractional System

This paper is concerned with the existence and uniqueness of positive solutions for a Volterra nonlinear fractional system of integral equations. Our analysis relies on a fixed point theorem of a sum operator. The conditions for the existence and uniqueness of a positive solution to the system are established. Moreover, an iterative scheme is constructed for approximating the solution. The case of quadratic system of fractional integral equations is also considered.

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