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 introduces general discrete linear Harniltonian eigenvalue problems and characterizes the eigenvalues. Assumptions are given, among them the new notion of strict controllability of a discrete system, that imply isolatedness and lower boundedness of the eigenvalues. Due to the quite general assumptions, discrete Sturrn-Liouville eigenvalue problems of higher order are included in the...

The measure algebras of the title are those which are also hypergroups with some regularity conditions, Examples include the convolutions associated with Jacobi polynomial series and Fourier Bessel series, It is shown here that there is a one-to-one correspondence between these hypergroups and a class of Sturm-Liouville problems which have the characters of the hypergroup as eigenfunctions, The...

It is well known that the two spectra {λn} and {μn} uniquely determine the potential function q (r) in a Sturm-Liouville equation defined on the unit interval having the singularity type ( ) 2 1 2 r r + +   (where  is a integer) at the point zero. In this work, we give the solution of the inverse problem on two partially noncoincide spectra for the Sturm-Liouville equation with the peculiari...

We consider the structure of the solution set of a nonlinear SturmLiouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of non-trivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, and we show that certain nodal properties of the solutions are preserved along these continua. Thes...

Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.

In this study we investigate asymptotic behavior of eigenvalues and eigenfunctions of one discontinuous Sturm-Liouville problem with eigendependent boundary and transmission conditions. c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.

We develop a numerical scheme for the wave front computation of complete transmissions and reflections in geometrical optics. Such a problem can be formulated by a reduced Liouville equation with a discontinuous local wave speed or index of refraction, arising in the high frequency limit of linear waves through inhomogeneous media. The key idea is to incorporate Snell’s Law of Refraction into t...

Abstract: In this paper, we present a novel method for computation of eigenvalues and eigenfunctions for a class of singular Sturm-Liouville boundary value problems using modified Adomian decomposition method. The proposed method can be applied to any type of regular as well as singular Sturm-Liouville problems. This current method is capable of finding any n-th eigenvalues and eigenfunctions o...