Quadratic functionals: positivity, oscillation, Rayleigh's principle

Werner Kratz

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Displaying similar documents to “Quadratic functionals: positivity, oscillation, Rayleigh's principle”

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Rayleigh principle for linear Hamiltonian systems without controllability

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In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems....