Existence of solutions for set differential equations involving causal operator with memory in Banach space

2012 ◽  
Vol 41 (1-2) ◽  
pp. 183-196 ◽  
Author(s):  
Jingfei Jiang ◽  
C. F. Li ◽  
H. T. Chen
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Causal Operator ◽  
With Memory

scholarly journals On the existence of solutions of differential equations of retarded type in a Banach space

1978 ◽  
Vol 35 (3) ◽  
pp. 253-260 ◽  
Author(s):  
V. Lakshmikantham ◽  
A. R. Mitchell ◽  
R. W. Mitchell
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Existence Of Solutions

scholarly journals Existence results for some differential equations with deviating argument

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 21-31 ◽  
Author(s):  
Monica Lauran
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Existence Results ◽  
Operator Technique ◽  
Nonexpansive Operator ◽  
Deviating Argument

In this paper we shall establish sufficient conditions for the existence of solutions of some differential equation and its solvability in CL, subset of the Banach space (C [a, b], ||?||). The main tool used in our study is the nonexpansive operator technique.

scholarly journals Existence of solutions to quasilinear differential equations in a Banach space

1976 ◽  
Vol 15 (3) ◽  
pp. 421-430
Author(s):  
James R. Ward
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Linear Systems ◽  
Function Space ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Reflexive Banach Space ◽  
Initial Value ◽  
Suitable Function

Initial value problems of the form x′ + A(t, x)x = f(t, x), x(0) = a, t ≥ 0, are considered in a real, separable, reflexive Banach space. Results concerning the existence of solutions on (0, ∞) are given by considering linear systems of the form x′ + A(t, u(t))x = f(t, u(t)). Here u(t) belongs to a suitable function space.

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.

Initial Value Problem of Fractional Integro-Differential Equations in Banach Space

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Adel Jawahdou
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Initial Value

AbstractThis paper is devoted to study the existence of solutions of nonlinear fractional integro-differential equation, via the techniques of measure of noncompactness. The investigation is based on a Schauder's fixed point theorem. The main result is less restrictive than those given in the literature. An illustrative example is given.

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