Compactness in certain abstract function spaces with application to differential inclusions

• Autorzy: N. U. Ahmed
• Języki publikacji: EN

Abstrakty

EN

In this note we present a result on compactness in certain Banach spaces of vector valued functions. We demonstrate an application of this result to the questions of existence of solutions of nonlinear differential inclusions on a Banach space.

Słowa kluczowe

EN

compactness; abstract function spaces; monotone operators; hemicontinuity; differential inclusions; existence of solutions

Kategorie tematyczne

• 93C25: Systems in abstract spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 34G99: None of the above, but in this section
• 46A50: Compactness in topological linear spaces; angelic spaces, etc.

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 75-94

Daty

wydano

1995

Twórcy

autor

N. U. Ahmed

• Department of Mathematics, Deprtament of Electrical Engineering, University of Ottawa, Canada

Bibliografia

• [1] L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS no 74, AMS, Providence, Rhode Island 1988.
• [2] N. U. Ahmed, Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions, International Symposium on Optimal Control of Differential Equations, (N. H. Pavel Ed.), Marcel Dekker Lecture Notes in Pure and Applied Mathematics 160 (1994), 1-19.
• [3] N. U. Ahmed, K. L .Teo, Optimal Control of Distributed Parameter Systems, Elsevier North Holland, New York, Oxford 1981.
• [4] N. H. Pavel, Nonlinear Evolution Operators and Semigroups, Springer Lecture Notes in Mathematices, 1260 Springer-Verlag 1980.
• [5] N. U. Ahmed, X. Xiang, Admissible relaxation in optimal control problems for infinite dimensional uncertian systems, Journal of Applied Mathematics and Stochastic Analysis 5 (1992), pp. 227-236.
• [6] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990.
• [7] D. H. Wagner, Survey of measurable selection theorems, SIAM Journal on Control and Optimization 15 (5) (1997), 859-903.
• [8] F. E. Browder, Nonlinear Operators and Nonlinear Evolution Equations in Banach Spaces, Proc. of Symp. in Pure and Appleid Math. Vol XVIII, Part 2, AMS, Providence, Rhode Island 1976.
• [9] J. P. Aubin, H. Frankowska, Set Valued Analysis , Birkhauser, Boston - Basil - Berlin 1990.
• [10] M. Kisielewicz Differential Inclusions and Optimal Control, PWN-Polish Scientific Publishers, Warszawa, Kluwer Academic Publishers, Dordrecht - Boston - London 1991.