Results 51 to 60 of about 14,640 (198)

Development of a methodology for transitioning from a spectral equation relative to a spatial variable to a differential equation relative to a spectral parameter in the Sturm-Liouville problem for a one-dimensional periodic two-layer photonic crystal

Вісник Харківського національногоуніверситету імені В.Н. Каразіна. Серія: Радіофізика та електроніка
Relevance. In connection with solving the problem of scattering of electromagnetic waves (diffraction problem) on objects such as photonic crystals (one-dimensional periodic unbounded), it is important to study the dispersion relation.
O. V. Kazanko, O. E. Penkina, O. V. Golovko   +2 more
doaj   +1 more source

Bound States of the Dirac Equation for a Class of Effective Quadratic Plus Inversely Quadratic Potentials

, 2003
The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless
Abramowitz, Antonio S.de Castro, Bagrov, Calogero, Calogero, Camiz, Constantinescu, de Castro, de Castro, de Castro, Dodonov, Gol’dman, Hall, Hall, Hall, Hall, Hall, Hall, Landau, Moshinsky, Nagiyev, Nogami, Pacheco, Pama, Peak, Strange, Szmytkowski, Thaller, Toyama, Toyama   +29 more
core   +1 more source

Inverse problems for Sturm-Liouville difference equations

Filomat, 2016
We consider a discrete Sturm-Liouville problem with Dirichlet boundary conditions. We show that the specification of the eigenvalues and weight numbers uniquely determines the potential. Moreover, we also show that if the potential is symmetric, then it is uniquely determined by the specification of the eigenvalues.
Bohner, Martin, Koyunbakan, Hikmet
openaire   +3 more sources

On the equivalence of discrete Sturm–Liouville problem with nonlocal boundary conditions to the algebraic eigenvalue problem

Lietuvos Matematikos Rinkinys, 2015
We consider the finite difference approximation of the second order Sturm–Liouville equation with nonlocal boundary conditions (NBC). We investigate the condition when the discrete Sturm–Liouville problem can be transformed to an algebraic eigenvalue ...
Jurij Novickij, Artūras Štikonas
doaj   +1 more source

A Study of the Eigenfunctions of the Singular Sturm–Liouville Problem Using the Analytical Method and the Decomposition Technique

Mathematics, 2020
The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov.
Oktay Sh. Mukhtarov, Merve Yücel
doaj   +1 more source

On completeness of weak eigenfunctions for multi-interval Sturm-Liouville equations with boundary-interface conditions

Demonstratio Mathematica, 2023
The goal of this study is to analyse the eigenvalues and weak eigenfunctions of a new type of multi-interval Sturm-Liouville problem (MISLP) which differs from the standard Sturm-Liouville problems (SLPs) in that the Strum-Liouville equation is defined ...
Olgar Hayati
doaj   +1 more source

Scattering theory for difference equations with operator coefficients

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We investigate a class of second‐order difference equations featuring operator‐valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi‐infinite square‐summable sequences with entries from a fixed Hilbert space ...
David Sher, Luis Silva, Boris Vertman, Monika Winklmeier   +3 more
wiley   +1 more source

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

, 2012
A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the
Apagyi B, Barnabás Apagyi, Coz M, De Alfaro V, Gelfand I M, Gelfand I M, Hilk D, Kuberczyk J, Levitan B M, Marchenko V A, Palmai T, Palmai T, Povzner A, Tamás Pálmai   +13 more
core   +1 more source

The Sturm-Liouville Hierarchy of Evolution Equations II

Advanced Nonlinear Studies, 2012
AbstractIn a previous paper [15] we introduced the Sturm-Liouville (SL) hierarchy of evolution equations. This hierarchy includes the Korteveg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchies. We also defined and discussed in detail the algebro-geometric solutions of the SL-hierarchy.
JOHNSON, RUSSELL ALLAN, L. Zampogni
openaire   +4 more sources

Spectral Parameter Power Series Representation for Regular Solutions of the Radial Dirac System

Mathematical Methods in the Applied Sciences, Volume 49, Issue 3, Page 2098-2113, February 2026.
ABSTRACT A spectral parameter power series (SPPS) representation for the regular solution of the radial Dirac system with complex coefficients is obtained, as well as a SPPS representation for the (entire) characteristic function of the corresponding spectral problem on a finite interval. Based on the SPPS representation, a numerical method for solving
Emmanuel Roque, Sergii M. Torba
wiley   +1 more source