On the correctness of nonlinear boundary value problems for systems of generalized ordinary differential equations

The concept of a strongly isolated solution of the nonlinear boundary value problem $$dx(t) = dA(t) cdot f(t,x(t)),h(x) = 0,$$ is introduced, whereA: [a, b]→R ^n×n is a matrix-function of bounded variation,f: [a, b]×R ⁿ →R ⁿ is a vector-function belonging to a Carathéodory class, andh a continuous operator from the space ofn-dimensional vector-functions of bounded variation intoR ⁿ . It is stated that the problems with strongly isolated solutions are correct. Sufficient conditions for the correctness of these problems are given.