Asymptotic properties of eigenvalues and eigenfunctions of a Sturm-Liouville problem with discontinuous weight function [PDF]
Miskolc Mathematical Notes, 2014 11 ...
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Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems
Communications on Pure and Applied Analysis, 2010 We are interested in the asymptotic profiles of all eigenfunctions for 1-dimensional linearized eigenvalue problems to nonlinear boundary value problems with a diffusion coefficient $\varepsilon$. For instance, it seems that they have simple and beautiful properties for sufficiently small $\varepsilon$ in the balanced bistable nonlinearity case.
Tohru Wakasa, Shoji Yotsutani
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Asymptotic analysis of the spectral Neumann problem in thick multi-structure of type 3:1:1
, 2005 The spectral Neumann problem is considered in a thick multi-structure, which is the union of some three-dimensional domain (the junction’s body) and a large number of ε-periodically situated thin cylinders along some curve (the joint zone) on the ...
Mel'nyk, T.A.
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On the solvability of the Sturm – Liouville problem, nonlinear in the spectral parameter
Известия высших учебных заведений. Поволжский регион: Физико-математические наукиBackground. The paper studies the solvability of the Sturm-Liouville problem, which is nonlinear in the spectral parameter. The problem is studied on a segment with boundary conditions of the third kind. Materials and methods.
G.V. Chalyshov
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Wave equation for Sturm-Liouville operator with singular potentials [PDF]
, 2022 The paper is denoted to the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with irregular (distributive) potentials.
Yeskermessuly, Alibek +2 more
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Pathological exponential asymptotics for a model problem of an equatorially trapped Rossby wave
, 2023 We examine a misleadingly simple linear second-order eigenvalue problem (the Hermite-with-pole equation) that was previously proposed as a model problem of an equatorially-trapped Rossby wave.
Trinh, Philippe H. +2 more
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Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields [PDF]
Transactions of the American Mathematical Society, 1996 We consider the Schrödinger operator with magnetic field, H = ( 1
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, 2010 We calculate the main asymptotic terms for eigenvalues, both simple and multiple, and eigenfunctions of the Neumann Laplacian in a three-dimensional domain $\Om(h)$ perturbed by a small (with diameter $O(h)$) Lipschitz cavern $\overline{\om_h}$ in a ...
Sokolowski, Jan +2 more
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Essentially isospectral transformations and their applications
, 2017 We define and study the properties of Darboux-type transformations between Sturm–Liouville problems with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions ...
Namig J. Guliyev
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Sharp Behavior of Dirichlet–Laplacian Eigenvalues for a Class of Singularly Perturbed Problems [PDF]
We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of the perturbed ...
Ognibene, Roberto, Abatangelo, Laura
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