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The paper deals with the impulsive nonlinear boundary value problemwhere J = [a, b], f ∈ Car(J × R 2 ), g 1 , g 2 ∈ C(R 2 ), I j , M j ∈ C(R). We prove the existence of a solution to this problem under the assumption that there exist lower and upper functions associated with the problem. Our proofs are based on the Schauder fixed point theorem and on the method of a priori estimates. No growth restrictions are imposed on f, g 1 , g 2 , I j , M j .

The paper deals with the second-order Dirichlet boundary value problem with one state-dependent impulseProofs 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. 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. MSC: 34B37; 34B15

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