Approximation of relaxed solutions for lower semicontinuous differential inclusions

A. Ornelas

Annales Polonici Mathematici (1991)

  • Volume: 56, Issue: 1, page 1-10
  • ISSN: 0066-2216

Abstract

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We construct a guided continuous selection for lsc multifunctions with decomposable values in L¹[0,T]. We then apply it to obtain a new result on the uniform approximation of relaxed solutions for lsc differential inclusions.

How to cite

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A. Ornelas. "Approximation of relaxed solutions for lower semicontinuous differential inclusions." Annales Polonici Mathematici 56.1 (1991): 1-10. <http://eudml.org/doc/262330>.

@article{A1991,
abstract = {We construct a guided continuous selection for lsc multifunctions with decomposable values in L¹[0,T]. We then apply it to obtain a new result on the uniform approximation of relaxed solutions for lsc differential inclusions.},
author = {A. Ornelas},
journal = {Annales Polonici Mathematici},
keywords = {differential inclusions; relaxed solutions; continuous selections},
language = {eng},
number = {1},
pages = {1-10},
title = {Approximation of relaxed solutions for lower semicontinuous differential inclusions},
url = {http://eudml.org/doc/262330},
volume = {56},
year = {1991},
}

TY - JOUR
AU - A. Ornelas
TI - Approximation of relaxed solutions for lower semicontinuous differential inclusions
JO - Annales Polonici Mathematici
PY - 1991
VL - 56
IS - 1
SP - 1
EP - 10
AB - We construct a guided continuous selection for lsc multifunctions with decomposable values in L¹[0,T]. We then apply it to obtain a new result on the uniform approximation of relaxed solutions for lsc differential inclusions.
LA - eng
KW - differential inclusions; relaxed solutions; continuous selections
UR - http://eudml.org/doc/262330
ER -

References

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  1. [1] H. A. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations 19 (1975), 386-398. 
  2. [2] J. P. Aubin and A. Cellina, Differential Inclusions, Springer, New York 1984. Zbl0538.34007
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  5. [5] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86. Zbl0677.54013
  6. [6] A. Cellina and M. V. Marchi, Non-convex perturbations of maximal monotone differential inclusions, Israel J. Math. 46 (1983), 1-11. Zbl0542.47036
  7. [7] G. Colombo, A. Fonda and A. Ornelas, Lower semicontinuous perturbations of maximal monotone differential inclusions, ibid. 61 (1988), 211-218. Zbl0661.47038
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  9. [9] A. Fryszkowski, Continuous selections for a class of non-convex multivalued maps, Studia Math. 76 (1983), 163-174. Zbl0534.28003
  10. [10] A. Fryszkowski, Continuous selections of Aumann integrals, J. Math. Anal. Appl., to appear. Zbl0704.28006
  11. [11] F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal. 7 (1977), 149-182. Zbl0368.60006
  12. [12] C. J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53-72. Zbl0296.28003
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  14. [14] C. Olech, Decomposability as a substitute for convexity, in: Multifunctions and Integrands, G. Salinetti (ed.), Lecture Notes in Math. 1091, Springer, Berlin 1984, 193-205. Zbl0592.28008
  15. [15] A. Ornelas, Parametrization of Carathéodory multifunctions, preprint SISSA 51 M (1988). 
  16. [16] G. Pianigiani, On the fundamental theory of multivalued differential equations, J. Differential Equations 25 (1977), 30-38. Zbl0398.34017
  17. [17] A. Pliś, Trajectories and quasitrajectories of an orientor field, Bull. Acad. Polon. Sci. 11 (1963), 369-370. Zbl0124.29404
  18. [18] A. A. Tolstonogov and I. A. Finogenko, On solutions of a differential inclusion with lower semicontinuous nonconvex right-hand side in a Banach space, Math. USSR-Sb. 53 (1986), 203-231. Zbl0588.34012
  19. [19] T. Ważewski, Sur une généralisation de la notion des solutions d'une équation au contingent, Bull. Acad. Pol. Sci. 10 (1962), 11-15. Zbl0104.30404

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