Asymptotic Approximations of Eigenvalues and Eigenfunctions for Regular Sturm-Liouville Problems

Eigenvalues of regular Sturm - Liouville problems

The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on the problem. An expression for the derivative of the n-th eigenvalue with respect to a given parameter: an endpoint, a boundary condition constant, a coefficient or weight function, is found.

Regular approximations of singular Sturm-Liouville problems

Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr} of regular S-L problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr} (ii) in the case when S is regular or limit-circle at each endpoint, a convergent sequence of ei...

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument

1 Department of Mathematics, Faculty of Arts and Science, Namik Kemal University, 59030 Tekirdağ, Turkey 2Department of Mathematics Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey 3 Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea 4Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaz...

Dependence of eigenvalues of Sturm-Liouville problems

The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on boundary points. The derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. This for arbitrary (separated or coupled) self-adjoint regular boundary conditions. In addition, as the length of the interval shrinks to zero all higher eigenvalues march o...