Representation of the set of mild solutions to the relaxed semilinear differential inclusion

2006 ◽  
Vol 26 (1) ◽  
pp. 143
Author(s):  
Irene Benedetti ◽  
Elena Panasenko
Keyword(s):  
Differential Inclusion ◽  
Mild Solutions ◽  
Semilinear Differential Inclusion

scholarly journals Trajectory approximately controllability and optimal control for noninstantaneous impulsive inclusions without compactness

2021 ◽  
pp. 1-31
Author(s):  
Shengda Liu ◽  
JinRong Wang ◽  
Donal O'Regan
Keyword(s):  
Optimal Control ◽  
Differential Inclusion ◽  
Regularity Condition ◽  
Measure Of Noncompactness ◽  
Lower Semicontinuous ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Semilinear Differential Inclusion ◽  
The Stability ◽  
Noninstantaneous Impulses

In this paper, a noninstantaneous impulsive differential inclusion model is established based on the heating phenomenon of the rod. The controllability problem for this system governed by a semilinear differential inclusion with noninstantaneous impulses is studied in a Banach space and in this differential inclusion system we assume that the semigroup generated by the linear part of the inclusion is not compact. We suppose that the set-valued nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness and some sufficient conditions for approximately controllability for both upper and almost lower semicontinuous types of nonlinearity are presented. Also we discuss existence and the stability of optimal control. As an application, the controllability for a differential inclusion system governed by a heat equation is considered.

scholarly journals Existence of mild solutions to semilinear fractional differential inclusion with deviated advanced nonlocal conditions

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Mohamed A. E. Herzallah ◽  
Ashraf H. A. Radwan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusion ◽  
Mild Solution ◽  
Nonlocal Condition ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Integral Form ◽  
Fractional Differential Inclusion ◽  
Fractional Differential

Abstract This paper is devoted to study the existence of at least one continuous mild solution to semilinear fractional differential inclusion with deviated-advanced nonlocal conditions. We develop the results obtained, by exchanging the deviated-advanced nonlocal condition to an integral form. Our results will be accomplished by using the nonlinear Leray-Schauder’s alternative fixed point theorem. The main results are well illustrated with the aid of an example.

scholarly journals Non-autonomous Second Order Differential Inclusions with a Stabilizing Effect

2020 ◽  
Vol 76 (1) ◽  
Author(s):  
Tiziana Cardinali ◽  
Eleonora De Angelis
Keyword(s):  
Banach Space ◽  
Wave Equation ◽  
Existence Theorem ◽  
Differential Inclusion ◽  
General Problem ◽  
Differential Inclusions ◽  
Mild Solutions ◽  
Second Order ◽  
Reaction Term ◽  
Stabilizing Effect

AbstractIn this paper we prove the existence of mild solutions for a problem governed by a semilinear non-autonomous second order differential inclusion where a stabilization of the solution is expected due to the control of the reaction term. In order to obtain our existence theorem, first we study a more general problem with a differential inclusion which involves a perturbation guided by an operator $$N :I \rightarrow C(C(I;X);X)$$ N : I → C ( C ( I ; X ) ; X ) , where X is a Banach space. Finally we show an illustrative example of application of our results to a problem involving a wave equation.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

MILD SOLUTIONS OF A FRACTIONAL PDE WITH NOISE

Authorea ◽  
2020 ◽  
Author(s):  
Noureddine Bouteraa ◽  
Mustafa Inc ◽  
Mehmet Ali Akinlar
Keyword(s):  
Mild Solutions ◽  
Fractional Pde

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

Existence of solutions for a second order boundary value problem with the Clarke subdifferential

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2763-2771 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
Samira Melit
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Lipschitzian Function ◽  
The Clarke Subdifferential

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.

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