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Abstract and Applied Analysis
Volume 2013, Article ID 892475, 6 pages
http://dx.doi.org/10.1155/2013/892475
Research Article

Impulsive Boundary Value Problems for Planar Hamiltonian Systems

Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

Received 3 September 2013; Accepted 24 October 2013

Academic Editor: Josef Diblik

Copyright © 2013 Zeynep Kayar and Ağacık Zafer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give an existence and uniqueness theorem for solutions of inhomogeneous impulsive boundary value problem (BVP) for planar Hamiltonian systems. Green's function that is needed for representing the solutions is obtained and its properties are listed. The uniqueness of solutions is connected to a Lyapunov type inequality for the corresponding homogeneous BVP.