Sturmian theory for linear Hamiltonian systems without controllability
Copyright policy )Sturmian theory for linear Hamiltonian systems without controllability
Summary: We present Sturmian separation and comparison theorems for linear Hamiltonian systems when no controllability assumption is imposed. This generalizes the traditional results of W. T. Reid for controllable (or normal) linear Hamiltonian systems to the possibly abnormal case. Our new theory is based on several recent results on linear Hamiltonian systems without controllability by W. Kratz, M. Wahrheit, V. Zeidan, and the author regarding the piecewise constant kernel for conjoined bases, the oscillation and eigenvalue theorems, and the Rayleigh principle.
- Masaryk University Czech Republic
Sturm-Liouville theory, Linear ordinary differential equations and systems, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
Sturm-Liouville theory, Linear ordinary differential equations and systems, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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