Geodesic
Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 273-287

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It is proved that in the space of Bochner-integrable mappings a multivalued mapping with nonconvex images has a continuous branch that, for a given single-valued mapping and for a previously specified accuracy, realizes the distance between the images of the single-valued mapping and the multivalued mapping. This result is applied to the investigation of properties of solutions of functional-differential inclusions with nonconvex right-hand side. 
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     author = {A. I. Bulgakov},
     title = {Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side},
     journal = {Sbornik. Mathematics},
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     volume = {71},
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     year = {1992},
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     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a0/}
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A. I. Bulgakov. Continuous branches of multivalued mappings and functional-differential inclusions with nonconvex right-hand side. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 273-287. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a0/