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 Article · Tue Jun 30 04:00:00 EDT 1998 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM1998V189N06ABEH000320; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202785

Bulgakov, A I; Tkach, L I ^[1]

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1. Tambov State University, Tambov (Russian Federation)

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.

• OSTI ID: 21202785
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 6 Vol. 189; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
DENSITY
FUNCTIONS
INTEGRALS
MAPS
MATHEMATICAL SOLUTIONS
PERTURBATION THEORY
VECTORS