scholarly journals A Nonlinear Integral Equation Related to Infectious Diseases

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Integral Equation ◽  
Infectious Diseases ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Numerical Algorithms ◽  
Data Dependence ◽  
Uniqueness Of Solutions

In this paper, a nonlinear integral equation related to infectious diseases is investigated. Namely, we first study the existence and uniqueness of solutions and provide numerical algorithms that converge to the unique solution. Next, we study the lower and upper subsolutions, as well as the data dependence of the solution.

scholarly journals On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Baghani ◽  
O. Baghani
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Operator

The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space . Later on, we give some examples of applications of this type of results.

Improved Integral Formulation for Acoustic Radiation Using Integral Equation of Frequency Averaged Quadratic Pressure

2017 ◽  
Vol 25 (01) ◽  
pp. 1750004 ◽  
Author(s):  
Honglin Gao ◽  
Sheng Li
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Acoustic Radiation ◽  
Boundary Integral ◽  
Uniqueness Of Solutions ◽  
High Frequencies ◽  
Numerical Examples ◽  
Integral Equation Formulation

This paper is concerned with the problem of obtaining a unique solution for radiation at irregular frequencies when an integral equation of frequency averaged quadratic pressure (FAQP) is used to get robust predictions at medium and high frequencies. It is proved that there is no unique solution of the integral equation of FAQP at irregular frequencies, and existence and uniqueness of solutions under four types of boundary conditions are discussed. A combined energy boundary integral equation formulation (CEBIEF) is presented and proves to be efficient to overcome the nonuniqueness of the integral equation of FAQP. The numerical examples are given to demonstrate the versatility of the CEBIEF method with a proposed function correctly indicating a solution.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

Existence and uniqueness of solutions for singular integral equation

Positivity ◽  
2008 ◽  
Vol 12 (4) ◽  
pp. 725-732 ◽  
Author(s):  
Zhongwei Cao ◽  
Daqing Jiang ◽  
Chengjun Yuan ◽  
Donal O’Regan
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions

QUANTUM INTEGRAL EQUATIONS OF VOLTERRA TYPE WITH GENERALIZED OPERATOR-VALUED KERNELS

2000 ◽  
Vol 03 (04) ◽  
pp. 505-517 ◽  
Author(s):  
ZHIYUAN HUANG ◽  
CAISHI WANG ◽  
XIANGJUN WANG
Keyword(s):  
Integral Equation ◽  
Explicit Expression ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Uniqueness Of Solutions ◽  
Volterra Type ◽  
Quantum Integral ◽  
Generalized Operator

Quantum integral equation of Volterra type with generalized operator-valued kernel is introduced. Existence and uniqueness of solutions are established, explicit expression of the solution is given, the continuity, continuous dependence on free terms and other properties of the solution are proved.

scholarly journals Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1253-1264 ◽  
Author(s):  
Hüseyin Işik ◽  
Duran Türkoğlu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Nonlinear Problems ◽  
Monotone Mappings ◽  
Mixed Monotone Property

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for mappings having a mixed monotone property in a complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

scholarly journals Recent Fixed-Point Results for θ − Contraction Mappings in Rectangular M − Metric Spaces with Supportive Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mustafa Mudhesh ◽  
Hasanen A. Hammad ◽  
Habes Alsamir ◽  
Muhammad Arshad ◽  
Eskandar Ameer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Theoretical Result ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Uniqueness Of The Solution

The goal of this manuscript is to present a new fixed-point theorem on θ − contraction mappings in the setting of rectangular M-metric spaces (RMMSs). Also, a nontrivial example to illustrate our main result has been given. Moreover, some related sequences with θ − contraction mappings have been discussed. Ultimately, our theoretical result has been implicated to study the existence and uniqueness of the solution to a nonlinear integral equation (NIE).

scholarly journals On the evolution equation with a dynamic Hardy-type potential

2021 ◽  
Author(s):  
Jann-Long Chern ◽  
Gyeongha Hwang ◽  
Jin Takahashi ◽  
Eiji Yanagida
Keyword(s):  
Integral Equation ◽  
Singular Point ◽  
Heat Equation ◽  
Existence And Uniqueness ◽  
Singular Potential ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Hardy Type ◽  
Radial Heat ◽  
Type Potential

Abstract Motivated by the celebrated paper of Baras and Goldstein (1984), we study the heat equation with a dynamic Hardy-type singular potential. In particular, we are interested in the case where the singular point moves in time. Under appropriate conditions on the potential and initial value, we show the existence, non-existence and uniqueness of solutions, and obtain a sharp lower and upper bound near the singular point. Proofs are given by using solutions of the radial heat equation, some precise estimates for an equivalent integral equation and the comparison principle.

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