Local mild solutions and impulsive mild solutions for semilinear Cauchy problems involving lower Scorza-Dragoni multifunctions

Tiziana Cardinali, Francesco Portigiani, Paola Rubbioni


In this note we investigate in Banach
spaces the existence of mild solutions for initial problems, also in
presence of impulses, governed by semilinear differential inclusions
where the non-linear part is a Scorza-Dragoni multifunction. All
the results are obtained via a generalization of {\it
Artstein-Prikry selection theorem} that we obtain in the first part
of the paper.


Semilinear differential inclusion; local; global and impulsive mild solution; Scorza-Dragoni multifunction; Carathéodory selection theorem

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