A new approach to BVPs with state-dependent impulses
Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, Olomouc, 771 46, Czech Republic
Boundary Value Problems 2013, 2013:22 doi:10.1186/1687-2770-2013-22Published: 11 February 2013
The paper deals with the second-order Dirichlet boundary value problem with one state-dependent impulse
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 . 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.