Compactness in certain abstract function spaces with application to differential inclusions

N. U. Ahmed

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1995)

  • Volume: 15, Issue: 1, page 75-94
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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N. U. Ahmed. "Compactness in certain abstract function spaces with application to differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.1 (1995): 75-94. <http://eudml.org/doc/275843>.

@article{N1995,
abstract = {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.},
author = {N. U. Ahmed},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {compactness; abstract function spaces; monotone operators; hemicontinuity; differential inclusions; existence of solutions},
language = {eng},
number = {1},
pages = {75-94},
title = {Compactness in certain abstract function spaces with application to differential inclusions},
url = {http://eudml.org/doc/275843},
volume = {15},
year = {1995},
}

TY - JOUR
AU - N. U. Ahmed
TI - Compactness in certain abstract function spaces with application to differential inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1995
VL - 15
IS - 1
SP - 75
EP - 94
AB - 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.
LA - eng
KW - compactness; abstract function spaces; monotone operators; hemicontinuity; differential inclusions; existence of solutions
UR - http://eudml.org/doc/275843
ER -

References

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  1. [1] L. C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS no 74, AMS, Providence, Rhode Island 1988. 
  2. [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. Zbl0854.49006
  3. [3] N. U. Ahmed, K. L .Teo, Optimal Control of Distributed Parameter Systems, Elsevier North Holland, New York, Oxford 1981. Zbl0472.49001
  4. [4] N. H. Pavel, Nonlinear Evolution Operators and Semigroups, Springer Lecture Notes in Mathematices, 1260 Springer-Verlag 1980. 
  5. [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. Zbl0777.93050
  6. [6] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990. Zbl0684.47029
  7. [7] D. H. Wagner, Survey of measurable selection theorems, SIAM Journal on Control and Optimization 15 (5) (1997), 859-903. Zbl0407.28006
  8. [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. Zbl0327.47022
  9. [9] J. P. Aubin, H. Frankowska, Set Valued Analysis , Birkhauser, Boston - Basil - Berlin 1990. 
  10. [10] M. Kisielewicz Differential Inclusions and Optimal Control, PWN-Polish Scientific Publishers, Warszawa, Kluwer Academic Publishers, Dordrecht - Boston - London 1991. 

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