Geodesic
Perturbation of a convex-valued operator by a set-valued map of Hammerstein type with non-convex values, and boundary-value problems for functional-differential inclusions
Sbornik. Mathematics, Tome 189 (1998) no. 6, pp. 821-848 Cet article a éte moissonné depuis la source Math-Net.Ru

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A functional inclusion in the space of continuous vector-valued functions on the interval $[a,b]$ is considered, the right-hand side of which is the sum of a convex-valued set-valued map and the product of a linear integral operator and a set-valued map with images convex with respect to switching. Estimates for the distance between a solution of this inclusion and a fixed continuous vector-valued function are obtained and the structure of the set of solutions of this inclusion is studied on the basis of these estimates. A result on the density of the solutions of this inclusion in the set of solutions of the 'convexized' inclusion is obtained and the 'bang-bang' principle for the original inclusion is established. This theory is applied to the study of the solution sets of boundary-value problems for functional-differential inclusions with non-convex right-hand sides. 
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     author = {A. I. Bulgakov and L. I. Tkach},
     title = {Perturbation of a~convex-valued operator by a~set-valued map of {Hammerstein} type with non-convex values, and boundary-value problems for functional-differential inclusions},
     journal = {Sbornik. Mathematics},
     pages = {821--848},
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     volume = {189},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_6_a0/}
}
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A. I. Bulgakov; L. I. Tkach. Perturbation of a convex-valued operator by a set-valued map of Hammerstein type with non-convex values, and boundary-value problems for functional-differential inclusions. Sbornik. Mathematics, Tome 189 (1998) no. 6, pp. 821-848. http://geodesic.mathdoc.fr/item/SM_1998_189_6_a0/

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