Near viability for fully nonlinear differential inclusions

2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Irina Căpraru ◽  
Alina Lazu
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Null Controllability ◽  
Dissipative Operator ◽  
Nonlinear Case ◽  
Tangency Condition ◽  
Gronwall’S Lemma ◽  
Nonlinear Differential Inclusions ◽  
Near Viability

AbstractWe consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.

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 An existence theorem for differential inclusions on Banach space

1992 ◽  
Vol 5 (2) ◽  
pp. 123-129 ◽  
Author(s):  
N. U. Ahmed
Keyword(s):  
Banach Space ◽  
Control Theory ◽  
Large Class ◽  
Existence Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Nonlinear Differential Inclusions

In this paper we consider the question of existence of solutions for a large class of nonlinear differential inclusions on Banach space arising from control theory.

scholarly journals On weak solutions of random differential inclusions

1995 ◽  
Vol 8 (4) ◽  
pp. 393-396
Author(s):  
Mariusz Michta
Keyword(s):  
Probability Measure ◽  
Differential Inclusion ◽  
Weak Solutions ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Initial Condition ◽  
Set Valued Mapping ◽  
Nonempty Compact ◽  
Convex Subsets

In the paper we study the existence of solutions of the random differential inclusion x˙t∈G(t,xt)     P.1,t∈[0,T]-a.e.x0=dμ, where G is a given set-valued mapping value in the space Kn of all nonempty, compact and convex subsets of the space ℝn, and μ is some probability measure on the Borel σ-algebra in ℝn. Under certain restrictions imposed on F and μ, we obtain weak solutions of problem (I), where the initial condition requires that the solution of (I) has a given distribution at time t=0.

scholarly journals Existence of solutions of functional stochastic differential inclusions

2002 ◽  
Vol 33 (1) ◽  
pp. 25-34 ◽  
Author(s):  
P. Balasubramaniam
Keyword(s):  
Fixed Point ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Analysis Approach ◽  
Point Analysis ◽  
Stochastic Differential Inclusions ◽  
Stochastic Differential Inclusion

In this paper, we prove the existence of solutions for functional stochastic differential inclusion via a fixed point analysis approach.

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.

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.

scholarly journals Positive Solvability for Conjugate Fractional Differential Inclusion of (k,n-k) Type without Continuity and Compactness

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 170
Author(s):  
Ahmed Salem ◽  
Aeshah Al-Dosari
Keyword(s):  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Inclusion Type ◽  
Fractional Differential Inclusion ◽  
Fractional Differential

The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the (k,n−k) conjugate fractional differential inclusion type with λ>0,1≤k≤n−1.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

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