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

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.


34G25 Evolution inclusions
Full Text: DOI


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