Boundary value problems for nonlinear impulsive Hamiltonian systems

•A nonlinear impulsive Hamiltonian system is studied.•An existence and uniqueness result is established.•Examples are given to illustrate the main result.•Spectral analysis is provided for the associated eigenvalue problem.

We study two point boundary value problems for nonlinear impulsive Hamiltonian systems. Spectral analysis of the corresponding linear impulsive Hamiltonian system and a fixed point theorem are employed to obtain an existence and uniqueness result for solutions of the nonlinear problem. Two examples are given in which the main condition is made explicit.