Differential equations with set-valued solutions |
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Authors: | T A Komleva A V Plotnikov N V Skripnik |
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Institution: | (1) Odessa National Polytechnic University, Odessa, Ukraine;(2) Odessa Academy of Civil Engineering and Architecture, Odessa, Ukraine;(3) Odessa National University, Odessa, Ukraine |
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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.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1326–1337, October, 2008. |
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Keywords: | |
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