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.

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. .

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.

On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order

2020 ◽  
Vol 26 (2) ◽  
pp. 263-272
Author(s):  
S. I. Unhale ◽  
Subhash D. Kendre
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Integrodifferential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThe objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.

scholarly journals Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1953
Author(s):  
Ning Ma ◽  
Zhen Wu
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Yosida Approximation ◽  
Uniqueness Of Solutions ◽  
Doubly Stochastic

In this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz condition. Moreover, thanks to the Yosida approximation, we solve such problem under monotone condition. Finally, we give the comparison theorems for such equations under the above two conditions respectively.

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

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