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

This paper deals with the existence of local and global mild solutions for the following semilinear evolution differential inclusion

x ' (t)A(t)x(t)+F(t,x(t))a.e.t[0,d],x(0)=x 0 E,

where {A(t)},t[0,d], is a family of linear operators in a Banach space E generating an evolution operator and F is a Carathéodory multifunction.

MSC:
34G25Evolution inclusions