Abstract
The paper is concerned with the evolution inclusionx′∈Ax+F(t,x), whereA generates a contractive semigroup andF is a lower semicontinuous multifunction. Constructing a suitable directionally continuous selection fromF, we prove the existence of solutions on a closed domain and the connectedness of the set of trajectories.
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Bressan, A., Staicu, V. On nonconvex perturbations of maximal monotone differential inclusions. Set-Valued Anal 2, 415–437 (1994). https://doi.org/10.1007/BF01026833
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DOI: https://doi.org/10.1007/BF01026833