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

Song Wen

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

Department of Mathematics, Harbin Normal University, Harbin, China

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.

Keywords

ENG

differential inclusion, relaxation theorem, well-posedness

J.-P. Aubin, Viability Theory, Birkhäuser, Boston, 1991.
J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin, 1984.
J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990.
A. Cellina and V. Staicu, Well posedness for differential inclusions on closed sets, J. Differential Equations 92 (1991), 2-13.
F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
H. Frankowska, A priori estimates for operational differential inclusions, J. Differential Equations 84 (1990), 100-128.
N. S. Papageorgiou, Relaxability and well-posedness for infinite dimensional optimal control problems, Indian J. Pure Appl. Math. 21 (1990), 513-526.
S. Shi, Viability theorems for a class of differential-operator inclusions, J. Differential Equations 79 (1989), 232-257.
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).
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).
Q. J. Zhu, On the solution set of differential inclusions in Banach space, J. Differential Equations 93 (1991), 213-237.

Title

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

Affiliations

Abstract

Keywords

Bibliography