A new approach to BVPs with state-dependent impulses

The paper deals with the second-order Dirichlet boundary value problem with one state-dependent impulse z ''(t) = f(t, z(t)) for a.e. t is an element of [0, T], z'(tau+) - z'(tau-) = I(z(tau)), tau = gamma(z(tau)), z(0) = 0, z(T) = 0. Proofs of the main results contain a new approach to boundary value problems with state-dependent impulses which is based on a transformation to a fixed point problem of an appropriate operator in the space C-1([0, T]) x C-1([0, T]). Sufficient conditions for the existence of solutions to the problem are given here. The presented approach can be extended to more impulses and to other boundary conditions.