Evolution inclusions in non separable Banach spaces

Francesco Saverio De Blasi; Giulio Pianigiani

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 227-250
  • ISSN: 0010-2628

Abstract

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We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.

How to cite

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De Blasi, Francesco Saverio, and Pianigiani, Giulio. "Evolution inclusions in non separable Banach spaces." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 227-250. <http://eudml.org/doc/248428>.

@article{DeBlasi1999,
abstract = {We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.},
author = {De Blasi, Francesco Saverio, Pianigiani, Giulio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {evolution inclusions; mild solutions; Lusin measurable multifunctions; Banach spaces; relaxation; evolution inclusions; mild solutions; Lusin measurable multifunctions; Banach spaces; relaxation},
language = {eng},
number = {2},
pages = {227-250},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Evolution inclusions in non separable Banach spaces},
url = {http://eudml.org/doc/248428},
volume = {40},
year = {1999},
}

TY - JOUR
AU - De Blasi, Francesco Saverio
AU - Pianigiani, Giulio
TI - Evolution inclusions in non separable Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 227
EP - 250
AB - We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.
LA - eng
KW - evolution inclusions; mild solutions; Lusin measurable multifunctions; Banach spaces; relaxation; evolution inclusions; mild solutions; Lusin measurable multifunctions; Banach spaces; relaxation
UR - http://eudml.org/doc/248428
ER -

References

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  1. Bressan A., Colombo G., Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86. (1988) Zbl0677.54013MR0947921
  2. Castaing C., Valadier M., Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin, 1977. Zbl0346.46038MR0467310
  3. De Blasi F.S., Pianigiani G., Hausdorff measurable multifunctions, J. Math. Anal. Appl. 228 (1998), 1-15. (1998) Zbl0921.54013MR1659936
  4. Filippov A.F., Classical solutions of differential equations with multivalued right hand side, SIAM J. Control Optim. 5 (1967), 609-621. (1967) MR0220995
  5. Frankowska H., A priori estimates for operational differential inclusions, J. Differential Equations 84 (1990), 100-128. (1990) Zbl0715.49010MR1042661
  6. Hermes H., The generalized differential equation x ' ∈ R ( t , x ) , Advances in Math. 4 (1970), 149-169. (1970) MR0252722
  7. Hille E., Phillips R.S., Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., Vol. 31, Providence R.I., 1957. Zbl0392.46001MR0089373
  8. Himmelberg C.J., Measurable relations, Fund. Math. 87 (1975), 53-72. (1975) Zbl0296.28003MR0367142
  9. Himmelberg C.J., Van Vleck F.S., Lipschitzian generalized differential equations, Rend. Sem. Mat. Univ. Padova 48 (1973), 159-169. (1973) Zbl0289.49009MR0340692
  10. Hu S., Lakshmikantham V., Papageorgiou N.S., On the solutions set of nonlinear differential inclusions, Dynamic Systems and Appl. 1 (1992), 71-82. (1992) MR1154650
  11. Klein E., Thompson A.C., Theory of correspondences, J. Wiley, New York, 1984. Zbl0556.28012MR0752692
  12. Kuratowski K., Ryll-Nardzewski C., A general theorem on selectors, Bull. Acad. Pol. Sci. Sér. Soc. Math. Astron. Phys. 13 (1965), 397-403. (1965) Zbl0152.21403MR0188994
  13. Papageorgiou N.S., Convexity of the orientor field and the solution set of a class of evolution inclusions, Math. Slovaca 43 (1993), 593-615. (1993) Zbl0799.34018MR1273713
  14. Papageorgiou N.S., A continuous version of the relaxation theorem for nonlinear evolution inclusions, Houston J. Math. 20 (1994), 685-704. (1994) Zbl0864.34057MR1305938
  15. Pazy A., Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, Berlin, 1983. Zbl0516.47023MR0710486
  16. Tolstonogov A.A., On the properties of integral solutions of differential inclusions with m -accretive operators, Soviet Math. Notes 49 (1991), 119-131. (1991) MR1135523

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