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Differential equations with set-valued solutions

Research paper by T. A. Komleva, A. V. Plotnikov, N. V. Skripnik

Indexed on: 27 Mar '09Published on: 27 Mar '09Published in: Ukrainian Mathematical Journal



Abstract

We consider a special space of convex compact sets and introduce the notions of derivative and integral for a set-valued mapping that differ from those already known. We also consider a differential equation with set-valued right-hand side satisfying the Carathéodory conditions and prove theorems on the existence and uniqueness of its solutions. This approach, in contrast to the Kaleva approach, enables one to consider fuzzy differential equations as ordinary differential equations with set-valued solutions.