Variations of a differential system containing discontinuities

The paper deals with differential equations with discontinuous right-hand sides. The variational equations for the partial derivatives of the solution with respect to the initial values are established. Formulae for the jump in the partial derivatives at the points where the right-hand side is discontinuous are derived. An application to a two-point boundary value problem is given. The theory is extended to allow general variations and transformations of variables at the points of discontinuity.