scholarly journals Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations

2010 ◽  
Vol 41 (4) ◽  
pp. 361-374
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Nonlocal Cauchy Problem

The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.

scholarly journals Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

2017 ◽  
Vol 4 (1) ◽  
pp. 1-15
Author(s):  
Machindra B. Dhakne ◽  
Poonam S. Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Strong Solutions ◽  
Fractional Power Of Operators

Abstract In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

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 Existence of solutions of nonlinear integrodifferential equation with nonlocal condition

1997 ◽  
Vol 10 (3) ◽  
pp. 279-288 ◽  
Author(s):  
K. Balachandran ◽  
M. Chandrasekaran
Keyword(s):  
Cauchy Problem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Global Solutions ◽  
Contraction Mapping Principle ◽  
Local And Global Solutions ◽  
Nonlocal Cauchy Problem

In this paper we prove the existence and uniqueness of local and global solutions of a nonlocal Cauchy problem for a class of integrodifferential equation. The method of semigroups and the contraction mapping principle are used to establish the results.

scholarly journals Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces

2003 ◽  
Vol 2003 (2) ◽  
pp. 65-79 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Schäuder Fixed Point Theorem

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed-point theorem. Examples are provided to illustrate the theory.

Existence and uniqueness of mild solution for fractional integrodifferential equations of neutral type with nonlocal conditions

2012 ◽  
Vol 62 (5) ◽  
Author(s):  
Fang Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Neutral Type ◽  
Nonlocal Conditions ◽  
Integrodifferential Equations

AbstractIn this paper, we prove the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations of neutral type with nonlocal conditions in a Banach space. New results are obtained by fixed point theorem.

scholarly journals Existence of solutions for neutral functional integrodifferential equations

2010 ◽  
Vol 41 (2) ◽  
pp. 117-128 ◽  
Author(s):  
R. Murugesu ◽  
S. Suguna
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Fractional Power ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Fractional Power Of Operators

In this paper, by using fractional power of operators and Sadovskii's fixed point theorem, we study the existence of mild and strong solutions of nonlinear neutral functional integrodifferential equations. The results we obtained are a generalization and continuation of the recent results on this issue.

scholarly journals On Existence and uniqueness to solutions nonlocal integrodifferential equations

2018 ◽  
Vol 1 (25) ◽  
pp. 493-508
Author(s):  
Fawzi Mutter Ismaael
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Necessary Conditions ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem

The Study aims in this paper to give and investigate the existence and uniqueness of mild solutions to nonlinear functional integrodifferential equations in Banach Spaces. the fixed point theorem, according to Sadovskii and sutible necessary conditions, are concepts consulted to obtain the results in the work

On the nonlocal Cauchy problem for semilinear fractional order evolution equations

2014 ◽  
Vol 12 (6) ◽  
Author(s):  
JinRong Wang ◽  
Yong Zhou ◽  
Michal Fečkan
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Growth Condition ◽  
Fractional Order ◽  
Point Theorem ◽  
Evolution Equations ◽  
Nonlocal Conditions ◽  
Time Interval ◽  
Nonlocal Cauchy Problem

AbstractIn this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first result relies on a growth condition on the whole time interval via Schaefer fixed point theorem. The second result relies on a growth condition splitted into two parts, one for the subinterval containing the points associated with the nonlocal conditions, and the other for the rest of the interval via O’Regan fixed point theorem.

scholarly journals A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Fang Li ◽  
Jin Liang ◽  
Tzon-Tzer Lu ◽  
Huan Zhu
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
The Fixed Point Theorem ◽  
Nonlocal Cauchy Problem ◽  
Condensing Maps

This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach spaceX. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a concrete integrodifferential equation is obtained.

scholarly journals RETRACTED ARTICLE: Existence and uniqueness of solutions for the Schrödinger integrable boundary value problem

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jianjie Wang ◽  
Ali Mai ◽  
Hong Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Linear Maps ◽  
Retracted Article

Abstract This paper is mainly devoted to the study of one kind of nonlinear Schrödinger differential equations. Under the integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz representations of linear maps and the Schrödinger fixed point theorem.

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