Rayleigh principle for linear Hamiltonian systems without controllability (Q2911445)
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scientific article; zbMATH DE number 6074761
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rayleigh principle for linear Hamiltonian systems without controllability |
scientific article; zbMATH DE number 6074761 |
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Rayleigh principle for linear Hamiltonian systems without controllability (English)
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31 August 2012
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linear Hamiltonian system
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Rayleigh principle
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self-adjoint eigenvalue problem
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proper focal point
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conjoined basis
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finite eigenvalue
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oscillation theorem
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normality
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quadratic functional
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0.89474887
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0.88660204
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0.8595886
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0.8539807
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0.8516797
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0.8404149
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0.8375175
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0.83505607
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The authors study linear Hamiltonian differential systems with Dirichlet boundary conditions without the controllability (or normality) assumption. They obtain the Rayleigh principle for these systems, which generalizes the known Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools are the extended Picone formula, results on piecewise constant kernels for conjoined bases of the Hamiltonian system, and an oscillation theorem. They also give an application of the main results.
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