PERTURBATION OF A CONVEX-VALUED OPERATOR BY A SET-VALUED MAP OF HAMMERSTEIN TYPE WITH NONCONVEX VALUES, AND BOUNDARY-VALUE-PROBLEMS FOR FUNCTIONAL-DIFFERENTIAL INCLUSIONS
Ai. Bulgakov et Li. Tkach, PERTURBATION OF A CONVEX-VALUED OPERATOR BY A SET-VALUED MAP OF HAMMERSTEIN TYPE WITH NONCONVEX VALUES, AND BOUNDARY-VALUE-PROBLEMS FOR FUNCTIONAL-DIFFERENTIAL INCLUSIONS, Sbornik. Mathematics, 189(5-6), 1998, pp. 821-848
A functional inclusion in the space of continuous vector-valued functi
ons on the interval [a,bl is considered, the right-hand side of which
is the sum of a convex-valued set-valued map and the product of a line
ar integral operator and a set-valued map with images convex with resp
ect to switching. Estimates for the distance between a solution of thi
s inclusion and a fixed continuous vector-valued function are obtained
and the structure of the set of solutions of this inclusion is studie
d on the basis of these estimates. A result on the density of the solu
tions of this inclusion in the set of solutions of the 'convexized' in
clusion is obtained and the 'bang-bang' principle for the original inc
lusion is established. This theory is applied to the study of the solu
tion sets of boundary-value problems for functional-differential inclu
sions with non-convex right-hand sides.