Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered. MSC-cl...

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The operator of double differentiation, perturbed by the composition differentiation and a convolution one, on finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability recovering kernel from spectrum in weighted $L_2$-norm norm. For this purpose, we successively prove each step algorithm for solving inverse problem both norms. Besides justifying numerical co...

We establish the connection between Sturm–Liouville equations on time scales and Sturm–Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm–Liouville equations on time scales which have been obtained by various authors in the past.

We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the orginal CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability ...

This paper deals with the problem of determining the leading coefficient k 1⁄4 kððu0ÞÞ of the nonlinear (monotone potential) Sturm–Liouville operator Au1⁄4 ðkððu0ÞÞu0ðxÞÞþ qðxÞuðxÞ, x2 ða;bÞ. As an additional condition only two measured data at the boundary (x1⁄4 a, x1⁄4 b) are used. Solvability and linearization of the corresponding nonlinear direct problem are given. An existence of a quasi-s...