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Keywords:
maximal monotone operator; differential inclusion; continuous selector; “bang-bang” principle
maximal monotone operator; differential inclusion; continuous selector; “bang-bang” principle
Summary:
We consider maximal monotone differential inclusions with memory. We establish the existence of extremal strong and then we show that they are dense in the solution set of the original equation. As an application, we derive a “bang-bang” principle for nonlinear control systems monitored by maximal monotone differential equations.
References:
[1] Aubin, J.-P., Cellina, A.: Differential Inclusions. Springer, Berlin, 1984. MR 0755330
[2] Baras, P.: Compacité de l’ opérateur $f \rightarrow u$ solution d’une equation nonlineaire $(du/dt)+ Au \ni f^{\prime \prime }$. C.R. Acad. Sci. Paris 286 (1978), 1113 - 1116. MR 0493554
[3] Benamara, M.: Points Extremaux, Multi-applications et Fonctionelles Intégrales. Thèse du 3ème cycle, Université de Grenoble (1975), France.
[4] Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values. Studia Math. 90 (1988), 69-85. MR 0947921
[5] Brezis, H.: Operateurs Maximaux Monotones. North Holland, Amsterdam, 1973. Zbl 0252.47055
[6] Dunford, N., Schwartz, J.: Linear Operators I. Willey, New York, 1958.
[7] Henry, C.: Differential equations with discontinuous right-hand side for planning procedures. J. Economic Theory 4 (1972), 545-551. MR 0449534
[8] Klein, E., Thompson, A.: Theory of Correspondences. Willey, New York, 1984. MR 0752692
[9] Moreau J.-J.: Evolution problem associated with a moving convex set in a Hilbert space. J. Diff. Equations 26 (1977), 347-374. MR 0508661
[10] Papageorgiou, N. S.: Convergence theorems for Banach space valued integrable multifunctions. Inter. J. Math. and Math. Sci. 10 (1987), 433-442. MR 0896595 | Zbl 0619.28009
[11] Papageorgiou, N. S.: On measurable multifunctions with applications to random multivalued equations. Math. Japonica 32 (1987), 437-464. MR 0914749 | Zbl 0634.28005
[12] Papageorgiou, N. S.: Differential inclusions with state constraints. Proc. Edinburgh Math. Soc. 32 (1988), 81-97. MR 0981995
[13] Papageorgiou, N. S.: Maximal monotone differential inclusions with memory. Proc. Indian Acad. Sci. 102 (1992), 59-72. MR 1163975 | Zbl 0758.34012
[14] Papageorgiou, N. S.: Convergence theorems for set-valued conditional expectations. Comm. Math. Univ. Carol. 34 (1) (1993), in press. MR 1240208 | Zbl 0788.60021
[15] Tolstonogov, A: Extreme continuous selectors for multivalued maps and “bang-bang" principle for evolution inclusion. Soviet Math. Doklady 317 (1991), 481-485. MR 1121349
[16] Wagner, D.: Survey of measurable selection theorems. SIAM J. Control and Optim. 15 (1977), 859-903. MR 0486391 | Zbl 0407.28006
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