Covering dimension and differential inclusions

Giovanni Anello

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 3, page 477-484
  • ISSN: 0010-2628

Abstract

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In this paper we shall establish a result concerning the covering dimension of a set of the type { x ∈ X : Φ ( x ) ∩ Ψ ( x ) ≠ ∅ } , where Φ , Ψ are two multifunctions from X into Y and X , Y are real Banach spaces. Moreover, some applications to the differential inclusions will be given.

How to cite

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Anello, Giovanni. "Covering dimension and differential inclusions." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 477-484. <http://eudml.org/doc/248612>.

@article{Anello2000,
abstract = {In this paper we shall establish a result concerning the covering dimension of a set of the type $\lbrace x\in X:\Phi (x)\cap \Psi (x)\ne \emptyset \rbrace $, where $\Phi $, $\Psi $ are two multifunctions from $X$ into $Y$ and $X$, $Y$ are real Banach spaces. Moreover, some applications to the differential inclusions will be given.},
author = {Anello, Giovanni},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {multifunction; Hausdorff distance; convex processes; covering dimension; differential inclusion; multifunction; Hausdorff distance; convex processes; covering dimension; differential inclusion},
language = {eng},
number = {3},
pages = {477-484},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Covering dimension and differential inclusions},
url = {http://eudml.org/doc/248612},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Anello, Giovanni
TI - Covering dimension and differential inclusions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 3
SP - 477
EP - 484
AB - In this paper we shall establish a result concerning the covering dimension of a set of the type $\lbrace x\in X:\Phi (x)\cap \Psi (x)\ne \emptyset \rbrace $, where $\Phi $, $\Psi $ are two multifunctions from $X$ into $Y$ and $X$, $Y$ are real Banach spaces. Moreover, some applications to the differential inclusions will be given.
LA - eng
KW - multifunction; Hausdorff distance; convex processes; covering dimension; differential inclusion; multifunction; Hausdorff distance; convex processes; covering dimension; differential inclusion
UR - http://eudml.org/doc/248612
ER -

References

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  2. Cubiotti P., Some remarks on fixed points of lower semicontinous multifunction, J. Math. Anal. Appl. (1993), 174 407-412. (1993) MR1215621
  3. Dzedzej Z., Gelman B.D., Dimension of the solution set for differential inclusions, Demonstratio Math. (1993), 26 1 149-158. (1993) Zbl0783.34008MR1226553
  4. Engelking R., Theory of Dimensions, Finite and Infinite, Heldermann Verlag, 1995. Zbl0872.54002MR1363947
  5. Gel'man P.D., On topological dimension of a set of solution of functional inclusions, Differential Inclusions and Optimal Control, Lecture Notes in Nonlinear Analysis, Torun, (1998), 2 163-178. (1998) 
  6. Klein E., Thompson A.C., Theory of Correspondences, John Wiley and Sons, 1984. Zbl0556.28012MR0752692
  7. Naselli Ricceri O., Classical solutions of the problem x ' ∈ F ( t , x , x ' ) , x ( t 0 ) = x 0 , x ' ( t 0 ) = y 0 , in Banach spaces, Funkcial. Ekvac. (1991), 34 1 127-141. (1991) MR1116885
  8. Ricceri B., Remarks on multifunctions with convex graph, Arch. Math. (1989), 52 519-520. (1989) Zbl0648.46010MR0998626
  9. Ricceri B., On the topological dimension of the solution set of a class of nonlinear equations, C.R. Acad. Sci. Paris, Série I (1997), 325 65-70. (1997) Zbl0884.47043MR1461399
  10. Ricceri B., Covering dimension and nonlinear equations, RIMS, Kyoto, Surikai sekikenkyusho-Kokyuroku (1998), 1031 97-100. (1998) Zbl0940.47049MR1662663

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