Univalence conditions and Sturm-Liouville eigenvalues

Univalence conditions and Sturm-Liouville eigenvalues

Multiplicity of Sturm-liouville Eigenvalues

The geometric multiplicity of each eigenvalue of a self-adjoint Sturm-Liouville problem is equal to its algebraic multiplicity. This is true for regular problems and for singular problems with limit-circle endpoints, including the case when the leading coefficient changes sign.

Eigenvalues of Sturm-liouville Problems with Discontinuous Boundary Conditions

For classical regular two-point self-adjoint Sturm-Liouville problems (SLP) the dependence of the eigenvalues on the boundary conditions is well understood because of some surprisingly recent results. Recently there has been a lot of interest in problems with discontinuous boundary conditions. Such conditions are known by various names including transmission conditions, interface conditions, po...

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

Sturm-liouville Problems and Discontinuous Eigenvalues

If a Sturm-Liouville problem is given in an open interval of the real line then regular boundary value problems can be considered on compact sub-intervals. For these regular problems, all with necessarily discrete spectra, the eigenvalues depend on both the end-points of the compact intervals, and upon the choice of the real separated boundary conditions at these end-points. These eigenvalues a...