This article is cited in 6 papers

On the theory of perturbed inclusions and its applications

A. I. Bulgakov, O. P. Belyaeva, A. A. Grigorenko

Tambov State University

Abstract: Inclusions with right-hand side that is the algebraic sum of the values of a compact-valued operator and a map equal to the product of a linear integral operator and a set-valued operator with values convex with respect to switching are considered. Existence questions for solutions of such inclusions are discussed, and the density principle and the ‘bang-bang’ principle are established. Properties of the solution sets of inclusions with internal and external perturbations are studied. A necessary and sufficient condition ensuring that the intersection of the closures of the sets of approximate solutions coincides with the closure of the set of the original inclusion is obtained. The results are applied to the analysis of boundary-value problems for functional-differential inclusions.

UDC: 517.9

MSC: Primary 47H04; Secondary 28B20, 34A60

Received: 20.04.2004 and 22.11.2004

DOI: 10.4213/sm1425

 English version: Sbornik: Mathematics, 2005, 196:10, 1421–1472

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