On the existence of mild solutions of semilinear evolution differential inclusions. (English) Zbl 1083.34046

Cardinali, Tiziana; Rubbioni, Paola

J. Math. Anal. Appl. 308, No. 2, 620-635 (2005); corrigendum and addendum, ibid. 438, No. 1, 514-517 (2016).

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.

Reviewer: Mouffak Benchohra (Sidi Bel Abbes)

MSC:

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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