Existence and controllability results for nonlinear differential inclusions with nonlocal conditions in Banach spaces. (English) Zbl 1037.34051

The existence and controllability of mild solutions to first-order semilinear evolution inclusions in a Banach space with nonlocal conditions are considered. The proofs of the main results are incorrect.
Under definitions and assumptions used in the paper, there is a lot of wrong statements and conclusions for the case of an infinite-dimensional space. For example, cited lemma 2.1 in [A. Lasota and Z. Opial, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 13, 781—786 (1965; Zbl 0151.10703)] for the infinite-dimensional space will be true if along with hypothesis (H2) the following assumptions are satisfied: the space is separable; the multifunction has convex weakly compact values; the multifunction is subordinated to an appropriate condition of growth. The estimates are and hence the proof of theorem 3.1 is wrong since the constant \(M\) in hypothesis (H5) depends on function \(y\), and so on.


34G25 Evolution inclusions
93B05 Controllability


Zbl 0151.10703
Full Text: DOI


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