In this paper we shall establish a result concerning the covering dimension of a set of the type $\{x\in X:\Phi (x)\cap \Psi (x)\neq \emptyset \}$, 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.
@article{119183, author = {Giovanni Anello}, title = {Covering dimension and differential inclusions}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {41}, year = {2000}, pages = {477-484}, zbl = {1038.47501}, mrnumber = {1795079}, language = {en}, url = {http://dml.mathdoc.fr/item/119183} }
Anello, Giovanni. Covering dimension and differential inclusions. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 477-484. http://gdmltest.u-ga.fr/item/119183/
Differential Inclusion, Springer Verlag, 1984. | MR 0755330
Some remarks on fixed points of lower semicontinous multifunction, J. Math. Anal. Appl. (1993), 174 407-412. (1993) | MR 1215621
Dimension of the solution set for differential inclusions, Demonstratio Math. (1993), 26 1 149-158. (1993) | MR 1226553 | Zbl 0783.34008
Theory of Dimensions, Finite and Infinite, Heldermann Verlag, 1995. | MR 1363947 | Zbl 0872.54002
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)
Theory of Correspondences, John Wiley and Sons, 1984. | MR 0752692 | Zbl 0556.28012
Classical solutions of the problem $x'\in F(t,x,x')$, $x(t_0)=x_0$, $x'(t_0)=y_0$, in Banach spaces, Funkcial. Ekvac. (1991), 34 1 127-141. (1991) | MR 1116885
Remarks on multifunctions with convex graph, Arch. Math. (1989), 52 519-520. (1989) | MR 0998626 | Zbl 0648.46010
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) | MR 1461399 | Zbl 0884.47043
Covering dimension and nonlinear equations, RIMS, Kyoto, Surikai sekikenkyusho-Kokyuroku (1998), 1031 97-100. (1998) | MR 1662663 | Zbl 0940.47049