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We consider a nonconvex and nonclosed semilinear differential inclusion and prove the arcwise connectedness of the set of its mild solutions. A similar result is provided for a class of nonconvex, nonclosed second order differential inclusions.
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Aurelian Cernea, On the solution set of some classes of nonconvex nonclosed differential inclusions. Port. Math. 65 (2008), no. 4, pp. 485–496DOI 10.4171/PM/1822