Data dependence of the solutions for set differential equations

Ioana Tise



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Let Rn be the real n-dimensional Euclidian space and Pcp,cv(Rn) the family of all nonempty compact, convex subsets of Rn endowed with the Pompeiu-Hausdorff metric H. Let I = [a, b] and X : I → Pcp,cv(Rn) be an operator. Hukuhara derivative of X might be introduced in the following way: DX(t) = lim h→0+ X(t + h) − X(t) h = lim h→0+ X(t) − X(t − h) h . We consider the Cauchy problem of the type  DX = F(t, X) X(0) = X0 where F : I × Pcp,cv(Rn) → Pcp,cv(Rn). The main purpose of the note is to study the data dependence of the solutions of the above problem.

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Tise, Ioana