A uniformly convergent series for Sturm-Liouville eigenvalues

Extremal Eigenvalues for a Sturm-Liouville Problem

We consider the fourth order boundary value problem (ry′′)′′+(py′)′+ qy = λwy, y(a) = y′(a) = y(b) = y′(b) = 0, which is used in a variety of physical models. For such models, the extremal values of the smallest eigenvalue help answer certain optimization problems, such as maximizing the fundamental frequency of a vibrating elastic system or finding the tallest column that will not buckle under...

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 fourth order Sturm-Liouville problems using Fliess series

We shall extend our previous results (Chanane, 1998) on the computation of eigenvalues of second order SturmLiouville problems to fourth order ones. The approach is based on iterated integrals and Fliess series. @ 1998 Elsevier Science B.V. All rights reserved. AMS classification: 34L15; 35C10

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

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...