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

Applicationes Mathematicae (1995)

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

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topWen, 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

top- [1] J.-P. Aubin, Viability Theory, Birkhäuser, Boston, 1991.
- [2] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin, 1984. Zbl0538.34007
- [3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990.
- [4] A. Cellina and V. Staicu, Well posedness for differential inclusions on closed sets, J. Differential Equations 92 (1991), 2-13. Zbl0731.34012
- [5] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983. Zbl0582.49001
- [6] H. Frankowska, A priori estimates for operational differential inclusions, J. Differential Equations 84 (1990), 100-128. Zbl0705.34016
- [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] S. Shi, Viability theorems for a class of differential-operator inclusions, J. Differential Equations 79 (1989), 232-257. Zbl0694.34011
- [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] 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] 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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