The solution set of a differential inclusionon a closed set of a Banach space

Song Wen

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 1, page 13-23
  • ISSN: 1233-7234

Abstract

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We consider differential inclusions with state constraints in a Banach space and study the properties of their solution sets. We prove a relaxation theorem and we apply it to prove the well-posedness of an optimal control problem.

How to cite

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Wen, Song. "The solution set of a differential inclusionon a closed set of a Banach space." Applicationes Mathematicae 23.1 (1995): 13-23. <http://eudml.org/doc/219112>.

@article{Wen1995,
abstract = {We consider differential inclusions with state constraints in a Banach space and study the properties of their solution sets. We prove a relaxation theorem and we apply it to prove the well-posedness of an optimal control problem.},
author = {Wen, Song},
journal = {Applicationes Mathematicae},
keywords = {differential inclusion; relaxation theorem; well-posedness; differential inclusion with state constraints; Banach space; optimal control problem},
language = {eng},
number = {1},
pages = {13-23},
title = {The solution set of a differential inclusionon a closed set of a Banach space},
url = {http://eudml.org/doc/219112},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Wen, Song
TI - The solution set of a differential inclusionon a closed set of a Banach space
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 1
SP - 13
EP - 23
AB - We consider differential inclusions with state constraints in a Banach space and study the properties of their solution sets. We prove a relaxation theorem and we apply it to prove the well-posedness of an optimal control problem.
LA - eng
KW - differential inclusion; relaxation theorem; well-posedness; differential inclusion with state constraints; Banach space; optimal control problem
UR - http://eudml.org/doc/219112
ER -

References

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  1. [1] J.-P. Aubin, Viability Theory, Birkhäuser, Boston, 1991. 
  2. [2] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin, 1984. Zbl0538.34007
  3. [3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990. 
  4. [4] A. Cellina and V. Staicu, Well posedness for differential inclusions on closed sets, J. Differential Equations 92 (1991), 2-13. Zbl0731.34012
  5. [5] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983. Zbl0582.49001
  6. [6] H. Frankowska, A priori estimates for operational differential inclusions, J. Differential Equations 84 (1990), 100-128. Zbl0705.34016
  7. [7] N. S. Papageorgiou, Relaxability and well-posedness for infinite dimensional optimal control problems, Indian J. Pure Appl. Math. 21 (1990), 513-526. Zbl0721.49007
  8. [8] S. Shi, Viability theorems for a class of differential-operator inclusions, J. Differential Equations 79 (1989), 232-257. Zbl0694.34011
  9. [9] A. A. Tolstonogov, The solution set of a differential inclusion in a Banach space. II, Sibirsk. Mat. Zh. 25 (4) (1984), 159-173 (in Russian). Zbl0537.34012
  10. [10] A. A. Tolstonogov and P. I. Chugunov, The solution set of a differential inclusion in a Banach space. I, ibid. 24 (6) (1983), 144-159 (in Russian). Zbl0537.34011
  11. [11] Q. J. Zhu, On the solution set of differential inclusions in Banach space, J. Differential Equations 93 (1991), 213-237. Zbl0735.34017

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