Lower semicontinuous differential inclusions. One-sided Lipschitz approach

Tzanko Donchev

Colloquium Mathematicae (1998)

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

Abstract

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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.

How to cite

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Donchev, 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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  1. [1] A. Bressan and V. Staicu, On nonconvex perturbation of maximal monotone differential inclusions, Set-Valued Anal. 2 (1994), 415-437. Zbl0820.47072
  2. [2] C G. Colombo, Approximate and relaxed solutions of differential inclusions, Rend. Sem. Mat. Univ. Padova 81 (1989), 229-238. Zbl0688.34007
  3. [3] D K. Deimling, Multivalued Differential Equations, de Gruyter, Berlin, 1992. 
  4. [4] T. Donchev, Functional differential inclusions with monotone right-hand side, Nonlinear Anal. 16 (1991), 533-542. Zbl0722.34010
  5. [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. [6] V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon, 1981. Zbl0456.34002
  7. [7] P N. Papageorgiou, A relaxation theorem for differential inclusions in Banach space, Tôhoku Math. J. 39 (1987), 505-517. Zbl0647.34011
  8. [8] A. Pliś, On trajectories of orientor fields, Bull. Acad. Polon. Sci. 13 (1965), 571-573. Zbl0138.34104
  9. [9] T A. Tolstonogov, Differential Inclusions in Banach Spaces, Novosibirsk, 1986 (in Russian). 
  10. [10] V V. Veliov, Differential inclusions with stable subinclusions, Nonlinear Anal. 23 (1994), 1027-1038. Zbl0816.34011

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