A second order differential inclusion with proximal normal cone in Banch spaces

2016 ◽  
Vol 44 (1) ◽  
pp. 143 ◽  
Author(s):  
Fatine Aliouane ◽  
Dalila Azzam-Laouir
Keyword(s):  
Differential Inclusion ◽  
Normal Cone ◽  
Second Order ◽  
Proximal Normal Cone

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.

Proximal Normal Cone Analysis on Smooth Banach Spaces and Applications

2014 ◽  
Vol 24 (1) ◽  
pp. 363-384 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Banach Spaces ◽  
Normal Cone ◽  
Proximal Normal Cone

A control problem governed by a second-order differential inclusion

2009 ◽  
Vol 88 (12) ◽  
pp. 1677-1690 ◽  
Author(s):  
Doria Affane ◽  
Dalila Azzam-Laouir
Keyword(s):  
Control Problem ◽  
Differential Inclusion ◽  
Second Order

scholarly journals Global Bifurcation for Second-Order Neumann Problem with a Set-Valued Term

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Ruyun Ma ◽  
Jiemei Li
Keyword(s):  
Neumann Problem ◽  
Differential Inclusion ◽  
Line Segment ◽  
Global Bifurcation ◽  
Second Order ◽  
Approximation Procedure ◽  
Bifurcation Theorem ◽  
Jump Discontinuities ◽  
Sturm Liouville

We study the global bifurcation of the differential inclusion of the form−(ku′)′+g(⋅,u)∈μF(⋅,u),  u′(0)=0=u′(1), whereFis a “set-valued representation” of a function with jump discontinuities along the line segment[0,1]×{0}. The proof relies on a Sturm-Liouville version of Rabinowitz's bifurcation theorem and an approximation procedure.

Impulsive differential inclusions via variational method

2017 ◽  
Vol 24 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Mouffak Benchohra ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Variational Method ◽  
Critical Point ◽  
Differential Inclusion ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Impulsive Differential Inclusions

AbstractIn this paper, we establish several results about the existence of second-order impulsive differential inclusion with periodic conditions. By using critical point theory, several new existence results are obtained. We also provide an example in order to illustrate the main abstract results of this paper.

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