On the Carathéodory superposition of multifunctions and an existence theorem

In: Mathematica Slovaca, vol. 64, no. 2

Grażyna Kwiecińska

Detaily:

Rok, strany: 2014, 315 - 332

Kľúčové slová:

multifunctions, continuity, measurability and integrability of multifunctions, derivative multifunctions, differential inclusions

DOI: https://doi.org/10.2478/s12175-014-0206-x

O článku:

Let $I\subset \RR$ be an interval and $Y$ a reflexive Banach space. We introduce the (H) property of a multifunction $F$ from $I\times Y$ 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 $f'(x)\in F(x,f(x))$ is given.

Ako citovať:

ISO 690:

Kwiecińska, G. 2014. On the Carathéodory superposition of multifunctions and an existence theorem. In Mathematica Slovaca, vol. 64, no.2, pp. 315-332. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0206-x

APA:

Kwiecińska, G. (2014). On the Carathéodory superposition of multifunctions and an existence theorem. Mathematica Slovaca, 64(2), 315-332. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0206-x

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