Abstract A new class of partial differential equations having symmetric orthogonal solutions is presented. The general equation presented and orthogonality obtained using the Sturm–Liouville approach. Conditions on polynomial coefficients to have admissible are given. case analyzed in detail, providing weight function, three-term recurrence relations for monic solutions, as well explicit form t...

Abstract In this paper, we are concerned with the eigenvalue gap and ratio of Dirichlet conformable fractional Sturm–Liouville problems. We show that kind differential equation satisfies property by Prüfer substitution. That is, n th eigenfunction has $n-1$ n − 1 zero in $( 0...

— This paper deals with the computation of the eigenvalues of non self-adjoint Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method. A few numerical examples among which singular ones will be presented to illustrate the merit of the method and comparison made with the exact eigenvalues when they are available.

The software package SLEDGE for Sturm-Liouville problems attempts to return eigenvalue and eigenfunction estimates within a user requested global error tolerance. The algorithm and underlying mathematics are discussed. Richardson's extrapolation plays a major role in this, but it must be carefully and conservatively implemented.

We describe relations between the Evans function, a modern tool in the study of stability of traveling waves and other patterns for PDEs, and the classical Weyl-Titchmarsh function for singular Sturm-Liouville differential expressions and for matrix Hamiltonian systems. Also, we discuss a related issue of approximating eigenvalue problems on the whole line by that on finite segments.

For any positive integer n and any given n distinct real numbers we construct a Sturm-Liouville problem whose spectrum is precisely the given set of n numbers. Such problems are of Atkinson type in the sense that the weight function or the reciprocal of the leading coefficient is identically zero on at least one subinterval.

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...