Dependence of Eigenvalues on the Problem
Copyright policy )Dependence of Eigenvalues on the Problem
AbstractThe eigenvalues of linear, regular, two point boundary value problems depend continuously on the problem. In the important self‐adjoint case studied by Naimark and Weidmann this dependence is differentiable and the derivatives of the eigenvalues with respect to a given parameter: an endpoint, a boundary condition, a coefficient, or the weight function, are found. Monotone properties of the eigenvalues with respect to the coefficients and the weight function are established without using the variational (min‐max) characterization.
- Northern Illinois University United States
- Northwestern University United States
linear boundary value problems, Sturm-Liouville theory, continuous dependence on parameters, eigenvalues, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, General spectral theory of ordinary differential operators
linear boundary value problems, Sturm-Liouville theory, continuous dependence on parameters, eigenvalues, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, General spectral theory of ordinary differential operators
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