Inequalities among eigenvalues of Sturm–Liouville problems with distribution potentials

Inequalities among eigenvalues of Sturm-Liouville problems

A New Proof of the Inequalities among Sturm-Liouville Eigenvalues

We consider self-adjoint regular Sturm-Liouville problems with positive leading coefficients and weight functions. A new proof of the inequalities among the eigenvalues for separated boundary conditions and those for coupled boundary conditions established recently by three of the authors with M. S. P. Eastham is given. This new proof does not assume that any special case of the inequalities ha...

Isoperimetric Inequalities and Eigenvalues

Isoperimetric Inequalities and Eigenvalues

An upper bound is given on the minimum distance between i subsets of the same size of a regular graph in terms of the i-th largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the i-th largest eigenvalue, for any integer i. Our bounds are shown to be asymptotically tight. A recent result by Quenell relating the diameter, the second eigenvalue, and the girth of a...

Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions