Existence and Controllability Results for Nonlinear Differential Inclusions with Nonlocal Conditions in Banach Spaces

2002 ◽  
Vol 8 (1) ◽  
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Nonlocal Conditions ◽  
Nonlinear Differential Inclusions

scholarly journals Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Alka Chadha ◽  
Rathinasamy Sakthivel ◽  
Swaroop Nandan Bora
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Nonlinear Differential Inclusions ◽  
Approximately Controllable ◽  
Fractional Differential

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.  

scholarly journals Evolution Inclusions in Banach Spaces under Dissipative Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 750
Author(s):  
Tzanko Donchev ◽  
Shamas Bilal ◽  
Ovidiu Cârjă ◽  
Nasir Javaid ◽  
Alina I. Lazu
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Qualitative Properties ◽  
Evolution Inclusions ◽  
Fully Nonlinear ◽  
Limit Solution ◽  
Nonlinear Differential Inclusions ◽  
Limit Solutions ◽  
Lipschitz Conditions ◽  
Integral Solutions

We develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties, replacing the commonly used compact or Lipschitz conditions by a dissipative one, i.e., one-sided Perron condition. Under some natural assumptions we prove that the set of limit solutions is the closure of the set of integral solutions.

scholarly journals On some evolution inclusions in non separable Banach spaces

2021 ◽  
Vol 66 (1) ◽  
pp. 17-27
Author(s):  
Aurelian Cernea
Keyword(s):  
Cauchy Problem ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
Differential Inclusions ◽  
Mild Solutions ◽  
Boundary Value ◽  
Nonlocal Conditions ◽  
Evolution Inclusion ◽  
Evolution Inclusions ◽  
Filippov Type

We study a Cauchy problem of a class of nonconvex second-order integro-differential inclusions and a boundary value problem associated to a semilinear evolution inclusion defined by nonlocal conditions in non-separable Banach spaces. The existence of mild solutions is established under Filippov type assumptions.

scholarly journals On The Existence of Solutions for Nonlinear Differential Inclusions

2015 ◽  
Vol 61 (1) ◽  
pp. 195-208 ◽  
Author(s):  
Irina Căpraru ◽  
Aurelian Cernea
Keyword(s):  
Cauchy Problem ◽  
Banach Spaces ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Nonlinear Differential Inclusions ◽  
Filippov Type

Abstract We consider a Cauchy problem for a nonlinear differential inclusion in separable and nonseparable Banach spaces under Filippov type assumptions and several existence results are obtained.

scholarly journals Controllability of Hilfer fractional noninstantaneous impulsive semilinear differential inclusions with nonlocal conditions

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
JinRong Wang ◽  
Gamal Ibrahim ◽  
Donal Donal O’Regan
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Nonlocal Conditions ◽  
Fractional Differential Inclusions ◽  
Impulsive Conditions ◽  
Fractional Differential

In this paper, we investigate the controllability of nonlocal Hilfer-type fractional differential inclusions with noninstantaneous impulsive conditions in Banach spaces.

Sign in / Sign up

Export Citation Format

Share Document