scholarly journals Existence of solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces

2003 ◽  
Vol 16 (2) ◽  
pp. 163-170 ◽  
Author(s):  
M. Kanakaraj ◽  
K. Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Topological Spaces ◽  
Sobolev Type ◽  
Multivalued Maps ◽  
Locally Convex

The existence of mild solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.

scholarly journals Multivalued impulsive neutral functional differential inclusions in Banach spaces

2002 ◽  
Vol 33 (1) ◽  
pp. 67-78
Author(s):  
M. Benchohra ◽  
J. Henderson ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Multivalued Maps ◽  
Functional Differential ◽  
Functional Differential Inclusions

In paper the existence of solutions for first and second order impulsive neutral functional differential inclusions in Banach spaces is investigated. The results are obtained by using a fixed point theorem for condensing multivalued maps due to Martelli and the semigroup theory.

scholarly journals Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

scholarly journals Existence of Mild Solutions for a Class of Impulsive Hilfer Fractional Coupled Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Karim Guida ◽  
Khalid Hilal ◽  
Lahcen Ibnelazyz ◽  
Ming Mei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Existence Results ◽  
Coupled Systems ◽  
Hilfer Fractional Derivative

The aim of this paper is to give existence results for a class of coupled systems of fractional integrodifferential equations with Hilfer fractional derivative in Banach spaces. We first give some definitions, namely the Hilfer fractional derivative and the Hausdorff’s measure of noncompactness and the Sadovskii’s fixed point theorem.

scholarly journals Existence of Solutions of a Class of Abstract Second Order Nonlinear Integrodifferential Equations

2002 ◽  
Vol 15 (2) ◽  
pp. 115-124 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Cosine Families ◽  
Schaefer Fixed Point Theorem ◽  
Families Of Operators

In this paper we prove the existence of solutions of nonlinear second order integrodifferential equations in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of operators and the Schaefer fixed point theorem.

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.

Controllability of Sobolev Type Semilinear Functional Differential and Integrodifferential Inclusions with an Unbounded Delay

2006 ◽  
Vol 13 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Yong-Kui Chang ◽  
Wan-Tong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Unbounded Delay ◽  
Functional Differential ◽  
The Fixed Point Theorem ◽  
Condensing Maps

Abstract In this paper, sufficient conditions are established for the controllability of Sobolev type semilinear functional differential and integrodifferential inclusions with an unbounded delay in Banach spaces. The main results are obtained by using the fixed point theorem for condensing maps due to Martelli.

A Fixed Point Theorem of Leggett–Williams Type with Applications to Single- and Multivalued Equations

2001 ◽  
Vol 8 (1) ◽  
pp. 13-25
Author(s):  
Ravi P. Agarwal ◽  
Donal O'regan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Multivalued Maps

Abstract We establish a general fixed point theorem for multivalued maps defined on cones in Banach spaces. Applications to single and multivalued equations are presented.

scholarly journals On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Fang Li ◽  
Ti-Jun Xiao ◽  
Hong-Kun Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Result ◽  
Infinite Delay ◽  
Mild Solutions

Of concern is a class of nonlinear neutral fractional integrodifferential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. An example is given to illustrate the existence result.

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

scholarly journals Existence of solutions to Sobolev-type partial neutral differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Shruti Agarwal ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Neutral Differential Equation ◽  
Sobolev Type ◽  
Neutral Differential Equations

This work is concerned with a nonlocal partial neutral differential equation of Sobolev type. Specifically, existence of the solutions to the abstract formulations of such type of problems in a Banach space is established. The results are obtained by using Schauder's fixed point theorem. Finally, an example is provided to illustrate the applications of the abstract results.

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