# Lower semicontinuous differential inclusions. One-sided Lipschitz approach

Colloquium Mathematicae (1998)

- Volume: 74, Issue: 2, page 177-184
- ISSN: 0010-1354

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topDonchev, Tzanko. "Lower semicontinuous differential inclusions. One-sided Lipschitz approach." Colloquium Mathematicae 74.2 (1998): 177-184. <http://eudml.org/doc/210508>.

@article{Donchev1998,

abstract = {Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.},

author = {Donchev, Tzanko},

journal = {Colloquium Mathematicae},

keywords = {differential inclusions; semicontinuous right-hand side; one-sided Lipschitz condition; Kamke function; quasitrajectory; optimal control theory},

language = {eng},

number = {2},

pages = {177-184},

title = {Lower semicontinuous differential inclusions. One-sided Lipschitz approach},

url = {http://eudml.org/doc/210508},

volume = {74},

year = {1998},

}

TY - JOUR

AU - Donchev, Tzanko

TI - Lower semicontinuous differential inclusions. One-sided Lipschitz approach

JO - Colloquium Mathematicae

PY - 1998

VL - 74

IS - 2

SP - 177

EP - 184

AB - Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.

LA - eng

KW - differential inclusions; semicontinuous right-hand side; one-sided Lipschitz condition; Kamke function; quasitrajectory; optimal control theory

UR - http://eudml.org/doc/210508

ER -

## References

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- [5] T. Donchev and R. Ivanov, On the existence of solutions of differential inclusions in uniformly convex Banach spaces, Mat. Balkanica 6 (1992), 13-24. Zbl0831.34013
- [6] V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon, 1981. Zbl0456.34002
- [7] P N. Papageorgiou, A relaxation theorem for differential inclusions in Banach space, Tôhoku Math. J. 39 (1987), 505-517. Zbl0647.34011
- [8] A. Pliś, On trajectories of orientor fields, Bull. Acad. Polon. Sci. 13 (1965), 571-573. Zbl0138.34104
- [9] T A. Tolstonogov, Differential Inclusions in Banach Spaces, Novosibirsk, 1986 (in Russian).
- [10] V V. Veliov, Differential inclusions with stable subinclusions, Nonlinear Anal. 23 (1994), 1027-1038. Zbl0816.34011

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