scholarly journals On stochastic integrodifferential equations via non-linear integral contractors II

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 81-92 ◽  
Author(s):  
Miljana Jovanovic ◽  
Svetlana Jankovic
Keyword(s):  
Lipschitz Condition ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Theorems ◽  
Volterra Integrodifferential Equation ◽  
Subject Classifications ◽  
Non Linear ◽  
Random Integral ◽  
Linear Integral ◽  
Mathematics Subject Classifications

The present paper represents a continuation of paper [4], in which the existence and uniqueness problems for a general Ito-Volterra integrodifferential equation are investigated by using the concept of a non-linear random integral contractor. Since the Lipschitz condition and the random integral contractor for the coefficients of the considered equation, in general, cannot be compared, the notions of the modified Lipschitz condition and modified integral contractor are introduced on some function spaces, as well as the conditions of their equivalence. Some existence and uniqueness theorems are also given. 2010 Mathematics Subject Classifications. 60H20. .

scholarly journals On stochastic integrodifferential equations via non-linear integral contractors I

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 167-180 ◽  
Author(s):  
Miljana Jovanovic ◽  
Svetlana Jankovic
Keyword(s):  
Lipschitz Condition ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Integrodifferential Equations ◽  
Uniqueness Of Solutions ◽  
Non Linear ◽  
Basic Ideas ◽  
Random Integral ◽  
Linear Integral ◽  
Special Case

The aim of this paper is to study the existence and uniqueness of solutions for a general stochastic integrodifferential equation of the Ito type, by using the concept of non-linear bounded random integral contractors, which includes the Lipschitz condition as a special case. The method applied in this consideration follows partially the basic ideas of the contractor theory introduced earlier by Altman [1, 2] and Kuo [6]. It is also shown that the Lipschitz condition and the condition based on a bounded random integral contractor for the coefficients of the considered equation, in general, cannot be compared.

On a class of Volterra and Fredholm non-linear integral equations

1976 ◽  
Vol 79 (2) ◽  
pp. 329-335 ◽  
Author(s):  
P. J. Bushell
Keyword(s):  
Integral Equations ◽  
Kernel Function ◽  
Existence And Uniqueness ◽  
Volterra Integral Equations ◽  
Fredholm Equations ◽  
Non Linear ◽  
Linear Volterra Integral Equations ◽  
Linear Integral ◽  
Image Position ◽  
Linear Integral Equations

This paper concerns the existence and uniqueness of non-negative solutions of non-linear Volterra integral equations of the typeandwhere the kernel function k(.,.) is non-negative and sufficiently smooth, and either 0 < p < 1 or – 1 < p < 1. We will consider also the corresponding Fredholm equationsand

NONLINEAR SINGULAR STURM-LIOUVILLE PROBLEMS WITH IMPULSIVE CONDITIONS

2019 ◽  
pp. 439
Author(s):  
Bilender P. Allahverdiev ◽  
Husein Tuna
Keyword(s):  
Existence And Uniqueness ◽  
Liouville Problem ◽  
Uniqueness Theorems ◽  
Impulsive Conditions ◽  
Limit Circle ◽  
Existence And Uniqueness Theorems ◽  
Non Linear ◽  
Limit Circle Case ◽  
Sturm Liouville ◽  
Circle Case

In this paper, we consider a non-linear impulsive Sturm-Liouville problem on semiinfinite intervals in which the limit-circle case holds at infinity for THE Sturm-Liouville expression. We prove the existence and uniqueness theorems for this problem.

scholarly journals Semilinear Volterra Integrodifferential Problems with Fractional Derivatives in the Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Mokhtar Kirane ◽  
Milan Medveď ◽  
Nasser-eddine Tatar
Keyword(s):  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Mild Solutions ◽  
Second Order ◽  
Classical Solutions ◽  
Volterra Integrodifferential Equation

A second-order semilinear Volterra integrodifferential equation involving fractional time derivatives is considered. We prove existence and uniqueness of mild solutions and classical solutions in appropriate spaces.

scholarly journals Existence and uniqueness of mild and strong solutions of nonlinear volterra integrodifferential equations in Banach spaces

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Semigroup Theory ◽  
Strong Solutions ◽  
Banach Fixed Point Theorem ◽  
Volterra Integrodifferential Equation

AbstractIn this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.

scholarly journals ON FRACTIONAL VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH FRACTIONAL INTEGRABLE IMPULSES

2019 ◽  
Vol 24 (3) ◽  
pp. 457-477 ◽  
Author(s):  
Sagar T. Sutar ◽  
Kishor D. Kucche Kucche
Keyword(s):  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Integrodifferential Equations ◽  
Compact Interval ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Volterra Integrodifferential Equation

We consider a class of nonlinear fractional Volterra integrodifferential equation with fractional integrable impulses and investigate the existence and uniqueness results in the Bielecki’s normed Banach spaces. Further, Bielecki-Ulam type stabilities have been demonstrated on a compact interval. A concrete example is provided to illustrate the outcomes we acquired.

Fixed points of set-valued F-contractions and its application to non-linear integral equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3377-3390 ◽  
Author(s):  
Satish Shukla ◽  
Dhananjay Gopal ◽  
Juan Martínez-Moreno
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Complete Metric Spaces ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Equations

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued ?-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed point theorems in metric spaces. Some examples are given to illustrate the new theory. Then we apply our results to establishing the existence and uniqueness of solutions for a certain type of non-linear integral equations.

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