Solvability of boundary value problems with continuous feedback

Abstract

In the theory of positional differential games [1–6], there are statements comparing results achievable in the classes of continuous strategies and program con� trols. Their detailed discussion can be found in [2, Section 55; 3, Section 3; 4, Sections 5, 6, 22, and 23; 5, pp. 232–239; 7–11]. In fact, these statements are concerned with a comparison of systems with contin� uous feedback and systems with open feedback, as well as with a comparison of the solvability of the corre� sponding boundary value problems of special form. This paper considers a nonlinear boundary value problem for a differential inclusion with a deviating