Controllability of Evolution Differential Inclusion with Nonlocal Condition in Banach Space

2017 ◽  
pp. 38-49
Author(s):  
Fan Guanghui ◽  
Yu Jinfeng ◽  
Song Qianhong
Keyword(s):  
Banach Space ◽  
Differential Inclusion ◽  
Nonlocal Condition

scholarly journals Existence of approximate solution to abstract nonlocal Cauchy problem

1992 ◽  
Vol 5 (4) ◽  
pp. 363-373 ◽  
Author(s):  
L. Byszewski
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Approximate Solution ◽  
Closed Subset ◽  
Nonlocal Condition ◽  
Right Hand ◽  
The Right ◽  
Nonlocal Cauchy Problem

The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].

Set of solutions of a differential inclusion in banach space. I

1984 ◽  
Vol 24 (6) ◽  
pp. 941-954 ◽  
Author(s):  
A. A. Tolstonogov ◽  
P. I. Chugunov
Keyword(s):  
Banach Space ◽  
Differential Inclusion

scholarly journals On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Irene Benedetti ◽  
Valeri Obukhovskii ◽  
Valentina Taddei
Keyword(s):  
Banach Space ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Nonlinear Term ◽  
Reflexive Banach Space ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fractional Differential ◽  
Partial Differential Inclusion ◽  
Generalized Boundary Condition

We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.

On Nonlinear Second Order Volterra-Fredholm Functional Integrodifferential Equation with Nonlocal Condition in Banach Spaces

2015 ◽  
Vol 54 (1) ◽  
pp. 75-96
Author(s):  
Machindra B. Dhakne ◽  
Poonam S. Bora
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Nonlocal Condition ◽  
Existence Of Solution ◽  
Second Order ◽  
Fredholm Functional

Abstract Our purpose in this paper is to study the existence of solution of nonlinear second order mixed functional integrodifferential equation with nonlocal condition in Banach space by employing two different techniques namely the Darbo-Sadovskii's fixed point theorem with Hausdorff's measure of noncompactness and the Leray Schauder Alternative.

On a fractional differential inclusion with integral boundary conditions in Banach space

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Phan Phung ◽  
Le Truong
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Differential Inclusion ◽  
Integral Boundary Conditions ◽  
Young Measures ◽  
Integral Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractWe consider a class of boundary value problem in a separable Banach space E, involving a nonlinear differential inclusion of fractional order with integral boundary conditions, of the form (*)$\left\{ \begin{gathered} D^\alpha u(t) \in F(t,u(t),D^{\alpha - 1} u(t)),a.e.,t \in [0,1], \hfill \\ I^\beta u(t)|_{t = 0} = 0,u(1) = \int\limits_0^1 {u(t)dt,} \hfill \\ \end{gathered} \right. $ where D α is the standard Riemann-Liouville fractional derivative, F is a closed valued mapping. Under suitable conditions we prove that the solutions set of (*) is nonempty and is a retract in W Eα,1(I). An application in control theory is also provided by using the Young measures.

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