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| We investigate the solvability of a differential system with general linear boundary conditions and state-dependent impulse conditions on a compact interval. This is the case when impulse moments satisfy a predetermined relation between state and time variables. The boundary conditions are expressed by a linear bounded operator on the space of left-continuous regulated vector-functions. Such operators are uniquely represented by a constant matrix and by the Kurzweil-Stieltjes integral of a matrix-function
whose elements have finite variation. Impulse points are determined as intersection points of a solution with barriers stated in a formulation of the boundary value problem. We provide transversality conditions which guarantee that each possible solution of the problem crosses each barrier at a unique point. Further, we construct a Banach space as a product space and an operator having a fixed point which consists from a finite number of functions. This number corresponds to a number of the barriers. The fixed point
can be used to a construction of a solution of the boundary value problem under consideration. |
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