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BY-NC-ND 3.0 license Open Access Published by De Gruyter May 8, 2014

On the Carathéodory superposition of multifunctions and an existence theorem

  • Grażyna Kwiecińska EMAIL logo
From the journal Mathematica Slovaca


Let I ⊂ ℝ be an interval and Y a reflexive Banach space. We introduce the (H) property of a multifunction F from I × Y to Y and prove that the Carathéodory superposition of F with each continuous function f from I to Y is a derivative provided that F has the (H) property. Some application of this theorem to the existence of solutions of differential inclusions f′(x) ∈ F(x, f(x)) is given.

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Published Online: 2014-5-8
Published in Print: 2014-4-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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