Scientific articles

Boundary value problems for functional-differential inclusions with the multivalued impulses

O. V. Filippova^ab, A. A. Grigorenko<sup>a

a</sup> Tambov State University named after G.R. Derzhavin
^b RUDN University

Abstract: The boundary value problems for a functional-differential inclusion generated by a multivalued map not necessarily convex-valued with respect to switching in the space of summable functions and with multi-valued impulses are considered. Concept of a generalized solution of such a problem is introduced. Existence conditions for a generalized solution of the boundary value problem are found. The effective estimates of generalized solutions are derived.

Keywords: functional-differential inclusion, boundary value problems, multi-valued impulses, convexity with respect to switching.

UDC: 517.911, 517.968

Received: 17.04.2017

DOI: 10.20310/1810-0198-2017-22-3-585-590