Duality Problems in the Convex Differential Inclusions of Elliptic Type

1. A. Kurzhanski, Set-valued Analysis and Differential Inclusions,Control
Theory(1993).
2. J.-L.Lions,Optimal Control of Systems Governed by Partial Differential Equations,
Springer, Berlin(1991).
{ } * * * * *
* * * *
, * * *
( ), ,
( , ) inf , , :
,
V
u w
M B v u A v
H u v u u Au Bw v w V
u Av
⎧⎪− = = < >−< + > ∈ =⎨
⎩⎪−∞ ≠
3. J.P. Aubin, A.Cellina , Differential Inclusion , Springer-Verlag , Grudlehnender
Math. , Wiss.,(1984).
4. R.T. Rockafellar, Convex Analysis , Second printing, Princeton University,
New Jersey(1972).
5. V.L. Makarov and A.M. Rubinov, The Mathematical Theory of Economic
Dynamics and Equilibrium , Nauka , Moscow ,1973, English transl., Springer-
Verlay ,Berlin (1977) .
6. F. H. Clarke , Optimization and Nomsmooth Analysis, John Wiley, New
York(1983).
7. I. Ekeland and R. Teman , Analyse Convexe et Problems Variationelles, Dunod
and Gauthier Villars , Paris (1972).
8. A.D. Ioffe and V.M. Tikhomirov, Theory of Extremal Problems, Nauka ,
Moscow ,1974(in Russian) ; English transl., North-Holland,Amsterdam,(1979).
9. B.S. Mordukhovich , Approximation Methods in Problems of Optimization
and Control, Nauka , Moscow, 1988; revised English transl. to appear , Wiley-
Interscience
10. B. N. Pshenichnyi , Convex Analysis and Extremal Problems, Nauka , Moscow,
1980(Russian)..
11. R.P.Agarwal, D,O’Regan,Fixed-point theory for weakly sequentially uppersemicontinuous
maps with applications to differential inclusions,Nonlinear Osccilations,
5(3)277-286(2002)
12. R. Vinter, Optimal Control, Birkhäuser Boston, ( 2000).
13. K. Wilfred, Maxima and Minima with applications, practical optimization
and duality, John Wiley and Sons, Inc., New York, 1999.
14. Wan-Xie Zhong, Duality System in Applied Mechanics and Optimal Control, Advances
in Mech. And Mathem. 5 (1992).
15. E.N.Mahmudov, Mathematical Analysis and Applications , Papatya, Istanbul(
2002).
16. E.N. Mahmudov [E.N. Makhmudov] , Optimization of discrete inclusions with
distributed parameters , Optimization 21), pp. 197-207, Berlin (1990).
17. E.N.Mahmudov, Duality in optimal control problems of optimal control described
by convex discrete and differential inclusions with delay, Automat Remote
Control 48(2)13-15(1987)
18. E.N.Mahmudov, Necessary and sufficient conditions for discrete and differential
inclusions of elliptic type, J.Mat.Appl.(323)768-789(2006)
19. E.N.Mahmudov, Locally adjoint mappings and optimization of the first boundary
value problems for hyperbolic type discrete and differential inclusions, Nonlin.
Anal.: Theory,Methods&Appl.67,pp.2966-2981(2007)
20. E.N.Mahmudov, On duality in problems of theory of convex difference
inclusions with aftereffect Different.Equat. pp. 1315-1324 (1987).
21. V.P.Mikhailov , Partial Differantial Equations , Nauka , Moscow ,1976, English
transl. MIR, Moscow, 1978.