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Keywords:
multifunction; Hausdorff distance; convex processes; covering dimension; differential inclusion
Summary:
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.
References:
[1] Aubin J.P., Cellina A.: Differential Inclusion. Springer Verlag, 1984. MR 0755330
[2] Cubiotti P.: Some remarks on fixed points of lower semicontinous multifunction. J. Math. Anal. Appl. (1993), 174 407-412. MR 1215621
[3] Dzedzej Z., Gelman B.D.: Dimension of the solution set for differential inclusions. Demonstratio Math. (1993), 26 1 149-158. MR 1226553 | Zbl 0783.34008
[4] Engelking R.: Theory of Dimensions, Finite and Infinite. Heldermann Verlag, 1995. MR 1363947 | Zbl 0872.54002
[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.
[6] Klein E., Thompson A.C.: Theory of Correspondences. John Wiley and Sons, 1984. MR 0752692 | Zbl 0556.28012
[7] Naselli Ricceri O.: 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. MR 1116885
[8] Ricceri B.: Remarks on multifunctions with convex graph. Arch. Math. (1989), 52 519-520. MR 0998626 | Zbl 0648.46010
[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. MR 1461399 | Zbl 0884.47043
[10] Ricceri B.: Covering dimension and nonlinear equations. RIMS, Kyoto, Surikai sekikenkyusho-Kokyuroku (1998), 1031 97-100. MR 1662663 | Zbl 0940.47049
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