Results 41 to 50 of about 8,236 (196)
On the inverse Sturm-Liouville problem
Discrete and Continuous Dynamical Systems, 2007 We pose and solve an inverse problem of an algebro-geometric type for the classical Sturm-Liouville operator. We use techniques of nonautonomous dynamical systems together with methods of classical algebraic geometry.
JOHNSON, RUSSELL ALLAN, L. ZAMPOGNI
openaire +3 more sources
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 +3 more
wiley +1 more source
Determination of source and variable coefficient in the inverse problem for the wave’s equation [PDF]
, 2017 Investigated the one-dimensional inverse problem with an unknown source and an unknown variable coefficient on two known solutions at fixed points in the plane.
Schabanova, G. I.
core +1 more source
Duality for an indefinite inverse Sturm–Liouville problem
Journal of Mathematical Analysis and Applications, 2005 It is solved an inverse problem associated with Sturm-Liouville equation with an indefinite weight function. A unique positive potential is reconstructed from two spectral sequences and a weight function given with a simple turning point in the interior of a finite interval with fixed end boundary conditions.
Jodayree Akbarfam, A. +1 more
openaire +2 more sources
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 +2 more
wiley +1 more source
Inverse Uniqueness in Interior Transmission Problem and Its Eigenvalue Tunneling in Simple Domain
Advances in Mathematical Physics, 2016 We study inverse uniqueness with a knowledge of spectral data of an interior transmission problem in a penetrable simple domain. We expand the solution in a series of one-dimensional problems in the far-fields.
Lung-Hui Chen
doaj +1 more source
Inverse indefinite Sturm–Liouville problems with three spectra
Journal of Mathematical Analysis and Applications, 2011 For the Sturm-Liouville problem \[ -y'' +q y = \lambda w y\text{ on }[a,b] \] with separated selfadjoint boundary conditions the inverse spectral question whether the potential \(q \in L^1(a,b)\) is uniquely determined by the spectrum is discussed. For the right definite case \(w > 0\), there are known results using two additional eigenvalue problems ...
Fu, Shouzhong +2 more
openaire +2 more sources
Spectral Parameter Power Series for Zakharov‐Shabat Direct and Inverse Scattering Problems
Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14661-14671, 15 November 2025.ABSTRACT We study the direct and inverse scattering problems for the Zakharov‐Shabat system. Representations for the Jost solutions are obtained in the form of the power series in terms of a transformed spectral parameter. In terms of that parameter, the Jost solutions are convergent power series in the unit disk.
Vladislav V. Kravchenko
wiley +1 more source
Reconstruction Techniques for Inverse Sturm–Liouville Problems With Complex Coefficients
Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 15875-15889, 30 November 2025.ABSTRACT A variety of inverse Sturm–Liouville problems is considered, including the two‐spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases, the potential in the Sturm–Liouville equation is assumed to be complex valued.
Vladislav V. Kravchenko
wiley +1 more source
Regularized Green's Function for the Inverse Square Potential
, 2002 A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version ...
CARLOS R. ORDÓÑEZ +5 more
core +1 more source