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Zbl 1083.34046
Cardinali, Tiziana; Rubbioni, Paola
On the existence of mild solutions of semilinear evolution differential inclusions.
(English)
[J] J. Math. Anal. Appl. 308, No. 2, 620-635 (2005). ISSN 0022-247X

This paper deals with the existence of local and global mild solutions for the following semilinear evolution differential inclusion $$x'(t)\in A(t)x(t)+F(t,x(t))\quad \text{a.e. } t\in [0,d],\quad x(0)=x_{0}\in E,$$ where $\{A(t)\}, \ t\in [0,d]$, is a family of linear operators in a Banach space $E$ generating an evolution operator and $F$ is a Carathéodory multifunction.
[Mouffak Benchohra (Sidi Bel Abbes)]
MSC 2000:
*34G25 Evolution inclusions

Keywords: semilinear evolution differential inclusion; mild solution; measure of noncompactness, condensing multimap; strongly measurable multifunction; upper semicontinuous multifunction

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