Abstract and Applied Analysis
Volume 2010 (2010), Article ID 514760, 18 pages
doi:10.1155/2010/514760
Research Article

Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Shurong Sun,1,2 Martin Bohner,2 and Shaozhu Chen3

1School of Science, University of Jinan, Jinan, Shandong 250022, China
2Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA
3Department of Mathematics, Shandong University in Weihai, Weihai, Shandong 264209, China

Received 2 December 2009; Accepted 17 February 2010

Academic Editor: Stevo Stevic

Copyright © 2010 Shurong Sun et al. 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 establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale 𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for 𝕋=ℝ and 𝕋=ℤ within one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i) M(λ) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.