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...

In recent years several high quality Sturm-Liouville software packages have been written (e.g., SLEDGE, SLEIGN, the NAG routine SL02FM). All excel at providing eigenfunction estimates at a nite set of points but only the NAG routine provides interpolation capability, and this by a fairly crude method (especially when compared with the sophistication of its eigenvalue solver). We describe an acc...

We consider the nonlinear Sturm-Liouville problem −(p(x)u′(x))′ + q(x)u(x) = f(x, u(x), u′(x)), in (0, π), (1) c00u(0) + c01u ′(0) = 0, c10u(π) + c11u ′(π) = 0, (2) where p ∈ C1[0, π], q ∈ C0[0, π], with p(x) > 0, x ∈ [0, π], and ci0 + ci1 > 0, i = 0, 1. We suppose that f : [0, π] × R2 → R is continuous and there exist increasing functions ζl, ζu : [0,∞) → R, and a constant B, such that limt→∞ ...

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

-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...

In this work, we study the following conformable fractional Sturm--Liouville
 problem
 \[
 l[y]=-T_{\alpha }(p(t)T_{\alpha }y(t))+q(t)y(t),
 \]
 where $t\in \lbrack 0,\infty ),$ real-valued functions $p$ and $q$
 satisfy conditions:
 \begin{array}{cc}
 (i) & q\in L_{\alpha }^{2}[0,\infty ), \\ 
 (ii) p\ \text{is\ absolutely\ continuous\ on}\ [0,\...

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, ...

The main purpose of this paper is to describe the extension of the successful modified integral series methods for Schrödinger problems to more general Sturm-Liouville eigenvalue problems. We present a robust and reliable modified Neumann method which can handle a wide variety of problems. This modified Neumann method is closely related to the second-order Pruess method, but provides for higher...