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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...
In 1996, H. Volkmer observed that the inequality
is satisfied with some positive constant for a certain class of functions f on [ − 1, 1] if the eigenfunctions of the problem
form a Riesz basis of the Hilbert space . Here the weight is assumed to satisfy a.e. on ( − 1, 1).
We present two criteria in terms of Weyl–Titchmarsh m‐functions for the Volkmer inequality...
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