Results 41 to 50 of about 15,725 (152)

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

New Results on a Nonlocal Sturm–Liouville Eigenvalue Problem with Fractional Integrals and Fractional Derivatives

Fractal and Fractional
In this paper, we investigate the eigenvalue properties of a nonlocal Sturm–Liouville equation involving fractional integrals and fractional derivatives under different boundary conditions.
Yunyang Zhang, Shaojie Chen, Jing Li
doaj   +1 more source

On the inverse scattering problem for Jacobi matrices with the spectrum on an interval, a finite system of intervals or a Cantor set of positive length

, 2001
Solving inverse scattering problem for a discrete Sturm-Liouville operator with the fast decreasing potential one gets reflection coefficients $s_\pm$ and invertible operators $I+H_{s_\pm}$, where $ H_{s_\pm}$ is the Hankel operator related to the symbol
Volberg, A., Yuditskii, P.
core   +2 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

Shape invariance through Crum transformation

, 2006
We show in a rigorous way that Crum's result on equal eigenvalue spectrum of Sturm-Liouville problems can be obtained iteratively by successive Darboux transformations. It can be shown that all neighbouring Darboux-transformed potentials of higher order,
Bagchi B. K., Cycon H. L., Darboux G., Gel’fand M., Gendenshtein L., Gendenshtein L., Gesztesy F., Gesztesy F., H. C. Rosu, Ince E. L., José Orlando Organista, Marchenko V. A., Marek Nowakowski   +12 more
core   +1 more source

Maxwell Fronts in the Discrete Nonlinear Schrödinger Equations With Competing Nonlinearities

Studies in Applied Mathematics, Volume 156, Issue 2, February 2026.
ABSTRACT In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schrödinger (DNLS) equations are often employed to model these dynamics, particularly in the context of Bose–Einstein condensates and optical ...
Farrell Theodore Adriano, Hadi Susanto
wiley   +1 more source

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

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

Generalized Hyers–Ulam Stability of Laplace Equation With Neumann Boundary Condition in the Upper Half‐Space

Mathematical Methods in the Applied Sciences, Volume 49, Issue 2, Page 521-530, 30 January 2026.
ABSTRACT This paper investigates the generalized Hyers–Ulam stability of the Laplace equation subject to Neumann boundary conditions in the upper half‐space. Traditionally, Hyers–Ulam stability problems for differential equations are analyzed by examining the system's error, particularly in relation to a forcing term.
Dongseung Kang, Hoewoon B. Kim, Dojin Kim   +2 more
wiley   +1 more source

Fundamentals of Right Hahn q‐Symmetric Calculus and Related Inequalities

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
Hahn symmetric quantum calculus is a generalization of symmetric quantum calculus. Motivated by the Hahn symmetric quantum calculus, we present the right Hahn symmetric derivative and integral, which are novel definitions for derivative and definite integral in Hahn symmetric quantum calculus.
Muhammad Nasim Aftab, Saad Ihsan Butt, Youngsoo Seol, Pengyu Chen   +3 more
wiley   +1 more source