BV solutions of multivalued differential equations on closed moving sets in Banach spaces

H. Benabdellah; C. Castaing; M. Gamal Ibrahim

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 53-81
  • ISSN: 0137-6934

Abstract

top
This paper is concerned with the existence of BV and right continuous solutions for some classes of multivalued differential equations on closed moving sets in Banach spaces.

How to cite

top

Benabdellah, H., Castaing, C., and Gamal Ibrahim, M.. "BV solutions of multivalued differential equations on closed moving sets in Banach spaces." Banach Center Publications 32.1 (1995): 53-81. <http://eudml.org/doc/262542>.

@article{Benabdellah1995,
abstract = {This paper is concerned with the existence of BV and right continuous solutions for some classes of multivalued differential equations on closed moving sets in Banach spaces.},
author = {Benabdellah, H., Castaing, C., Gamal Ibrahim, M.},
journal = {Banach Center Publications},
keywords = {BV and right continuous solutions; multivalued differential equations on closed moving sets; Banach spaces},
language = {eng},
number = {1},
pages = {53-81},
title = {BV solutions of multivalued differential equations on closed moving sets in Banach spaces},
url = {http://eudml.org/doc/262542},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Benabdellah, H.
AU - Castaing, C.
AU - Gamal Ibrahim, M.
TI - BV solutions of multivalued differential equations on closed moving sets in Banach spaces
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 53
EP - 81
AB - This paper is concerned with the existence of BV and right continuous solutions for some classes of multivalued differential equations on closed moving sets in Banach spaces.
LA - eng
KW - BV and right continuous solutions; multivalued differential equations on closed moving sets; Banach spaces
UR - http://eudml.org/doc/262542
ER -

References

top
  1. [AVC] A. Amrani, C. Castaing et M. Valadier, Convergence forte dans L 1 impliquée par la convergence faible. Méthodes de troncature, C. R. Acad. Sci. Paris Sér. I 314 (1992), 37-40. Zbl0768.46002
  2. [AC] J.-P. Aubin and A. Cellina, Differential Inclusions. Set-Valued Maps and Viability Theory, Springer, Berlin, 1984. Zbl0538.34007
  3. [BP] C. Bardaro and P. Pucci, Some contributions to the theory of multivalued differential equations, Atti Sem. Mat. Fis. Univ. Modena 32 (1983), 175-202. Zbl0542.34009
  4. [B] J. M. Bony, Principe de maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier 19 (1969), 277-304. Zbl0176.09703
  5. [Br] H. Brezis, On a characterization of flow invariant sets, Comm. Pure Appl. Math. 23 (1970), 261-263. Zbl0191.38703
  6. [BCS] P. Brandi, L. Cesari and A. Salvadori, Existence theorems, converging simple integrals of the calculus of variations for discontinuous solutions, Arch. Rational Mech. Anal. 98 (1987), 285-396. 
  7. [Ca1] C. Castaing, Quelques résultats de compacité liés à l'intégration, C. R. Acad. Sci. Paris Sér. A 270 (1970), 1732-1735. Zbl0195.40704
  8. [Ca2] C. Castaing, Equation différentielle multivoque avec contrainte sur l'état dans les espaces de Banach, Sém. d'Analyse Convexe Montpellier (1978), exp. 13 et C. R. Acad. Sci. Paris Sér. A 288 (1979), 507-509. 
  9. [Ca3] C. Castaing, Quelques résultats de convergence des suites adaptées, Sém. d'Analyse Convexe Montpellier (1987), exp. 2 (24 pages) et Acta Math. Vietnam. 14 (1989), 51-66. 
  10. [CV] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977. Zbl0346.46038
  11. [De1] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lecture Notes in Math. 596, Springer, Berlin, 1985. 
  12. [De2] K. Deimling, Multivalued differential equations on closed sets, Differential and Integral Equations 1 (1988), 23-30. 
  13. [EJ] H. W. Ellis and R. L. Jeffery, Derivatives and integrals with respect to a base function of generalized bounded variation, Canad. J. Math. 19 (1967), 225-241. Zbl0156.06004
  14. [G] A. Grothendieck, Espaces Vectoriels Topologiques, Publ. Soc. Math. Sao Paulo, 1954. 
  15. [J] R. L. Jeffery, Non-absolutely convergent integrals with respect to functions of bounded variation, Trans. Amer. Math. Soc. 34 (1932), 645-675. Zbl58.0254.02
  16. [L] M. Larrieu, Invariance d'un fermé pour un champ de vecteurs de Carathéodory, Publ. Math. Univ. Pau, 1987. 
  17. [Ma] R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Krieger, Malabar, Fla., 1987. 
  18. [Me] H. Methlouthi, Equations différentielles multivoques sur un graphe localement compact, Cahiers Math. de la Décision 7713 (1977). Zbl0355.34003
  19. [MM] M. D. P. Monteiro Marquès, Perturbations convexes semi-continues supérieurement de problèmes d'évolution dans les espaces de Hilbert, Sém. d'Analyse Convexe Montpellier (1984), exp. 2 (23 pages). 
  20. [M1] J. J. Moreau, Sur les mesures différentielles des fonctions vectorielles à variation localement bornée, Sém. d'Analyse Convexe Montpellier (1975), exp. 17 (39 pages). 
  21. [M2] J. J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, J. Differential Equations 26 (1977), 347-374. Zbl0356.34067
  22. [MV1] J. J. Moreau et M. Valadier, Dérivation d'une mesure vectorielle sur un intervalle, Sém. d'Analyse Convexe Montpellier (1984), exp. 1 (14 pages). 
  23. [MV2] J. J. Moreau et M. Valadier, Quelques résultats sur les fonctions vectorielles à variation bornée d'une variable réelle, Sém. d'Analyse Convexe Montpellier (1984), exp. 2 (16 pages). 
  24. [MV3] J. J. Moreau et M. Valadier, A chain rule involving vector functions of bounded variation, J. Funct. Anal. 74 (1987), 333-345. Zbl0632.46040
  25. [MO] M. Moussaoui, Approximations lipschitziennes de multifonctions et application à la relaxation de certains problèmes de contrôle optimal et de calcul de variations, Thèse, Université Montpellier II, 1990 (159 pages). 
  26. [N] M. Nagumo, Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen, Proc. Math. Soc. Japan 24 (1942), 555-559. 
  27. [T] A. A. Tolstonogov, On the structure of the solutions set for differential inclusions in a Banach space, Mat. Sb. 118 (1982), 3-18 (in Russian); English transl. in Math. USSR-Sb 46 (1983). Zbl0514.34053
  28. [V] M. Valadier, Applications des mesures de Young aux suites uniformément intégrables dans un Banach séparable, Sém. d'Analyse Convexe Montpellier (1990), exp. 3 (14 pages). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.