Extremal solutions for nonlinear second order differential inclusions

2005 ◽  
Vol 278 (1-2) ◽  
pp. 43-52 ◽  
Author(s):  
P. Douka ◽  
N. S. Papageorgiou
Keyword(s):  
Differential Inclusions ◽  
Second Order ◽  
Extremal Solutions

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.

scholarly journals Some nonoscillation criteria for inclusions

2006 ◽  
Vol 80 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Said R. Grace ◽  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Second Order ◽  
Upper Semicontinuous ◽  
Semicontinuous Multifunctions

AbstractNew nonoscillatory criteria are presented for second order differential inclusions. The theory relies on Ky Fan's fixed point theorem for upper semicontinuous multifunctions.

PERIODIC SOLUTIONS OF SECOND-ORDER DIFFERENTIAL INCLUSIONS SYSTEMS WITH (q, p)-LAPLACIAN

2011 ◽  
Vol 09 (02) ◽  
pp. 201-223 ◽  
Author(s):  
DANIEL PAŞCA
Keyword(s):  
Periodic Solutions ◽  
Differential Inclusions ◽  
Existence Results ◽  
Second Order

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with (q, p)-Laplacian.

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