Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions (Q440710)

The authors first establish oscillation theorems, Rayleigh principle, and coercivity results for continuous-time linear Hamiltonian systems and discrete symplectic systems with general boundary conditions, i.e., for the cases of separated and jointly varying endpoints (including the periodic boundary conditions as a special case), and with no controllability (normality) and strong observability assumptions. Second, they extend those results to symplectic dynamic systems on time scales by considering the time interval as a time scale and applying suitable time scales techniques to reduce the problem with jointly varying endpoints into a problem with separated endpoints, and then into a problem with Dirichlet boundary conditions which was discussed before by them. The present work shows the utility and power of the analysis on time scales in studying the continuous- and discrete-time theories.