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generalized differential equations; adjoint operators; existence and uniqueness theorems; controllability; regulated function; boundary value problem; adjoint problem; interface problem; Peron-Stieltjes integral; Kurzweil integral
Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily of bounded variation). Similar problems in the space of regulated functions were treated e.g. by Ch. S. Hönig, L. Fichmann and L. Barbanti, who made use of the interior (Dushnik) integral. In this paper the integral is the Perron-Stieltjes (Kurzweil) integral.
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