Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

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.

This paper gives constructive algorithms for the classical inverse Sturm-Liouville problem. It is shown that many of the formulations of this problem are equivalent to solving an overdetermined boundary value problem for a certain hyperbolic operator. Two methods of solving this latter problem are then provided, and numerical examples are presented.

The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

in this work, we study the performance of the sinc-collocation method for solving bratu's problem. for different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. the comparison of the obtained results veri ed that this method converges to the exact solution rapidly and with

We consider a Sturm-Liouville boundary value problem in a bounded domain D of Rn. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on ∂D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the me...

We nd the adjoint of the Askey-Wilson divided di erence operator with respect to the inner product on L 2 ( 1; 1; (1 x 2 ) 1=2 dx) de ned as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic de...

— 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.

We present a new approach to the numerical solution of Sturm{Liouville eigenvalue problems based on Magnus expansions. Our algorithms are closely related to Pruess' methods [Pre73], but provide for high order approximations at nearly the same cost as the second-order Pruess method. By using Newton iteration to solve for the eigenvalues, we are able to present an e cient algorithm for computing ...