Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Mathematische Nachrichten |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1002/mana.201200314 |
| Field | General mathematics |
| Keywords | Linear Hamiltonian system; Comparison of eigenvalues; Finite eigenvalue; Sturmian comparison theorem; Controllability; Strict normality; Self-adjoint eigenvalue problem; Oscillation theorem |
| Attached files | |
| Description | In this work we derive new comparison results for (finite) eigenvalues of two self-adjoint linear Hamiltonian eigenvalue problems. The coefficient matrices depend on the spectral parameter nonlinearly and the spectral parameter is present also in the boundary conditions. We do not impose any controllability or strict normality assumptions. Our method is based on a generalization of the Sturmian comparison theorem for such systems. The results are new even for the Dirichlet boundary conditions, for linear Hamiltonian systems depending linearly on the spectral parameter, and for Sturm-Liouville eigenvalue problems with nonlinear dependence on the spectral parameter. |
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