Boundary Value Problems–Hamiltonian Systems

2009 ◽  
pp. 351-454
Author(s):  
Nikolaos S. Papageorgiou ◽  
Sophia Th. Kyritsi-Yiallourou
Keyword(s):  
Boundary Value Problems ◽  
Hamiltonian Systems ◽  
Boundary Value

scholarly journals Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Shurong Sun ◽  
Martin Bohner ◽  
Shaozhu Chen
Keyword(s):  
Boundary Value Problems ◽  
Spectral Theory ◽  
Hamiltonian Systems ◽  
Dynamic Systems ◽  
Time Scale ◽  
Boundary Value ◽  
Hamiltonian Dynamic ◽  
Special Cases ◽  
Linear Hamiltonian Systems ◽  
Singular Hamiltonian Systems

We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for𝕋=ℝand𝕋=ℤwithin 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.

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