Spectral asymptotics of solutions of a \(2\times 2\) system of first-order ordinary differential equations
type: Item
instance of: scholarly article
title: Spectral asymptotics of solutions of a \(2\times 2\) system of first-order ordinary differential equations
zbMATH Open document ID: 1494.34087
DOI: 10.1134/S0001434621110353
author: A. P. Kosarev
author: A. A. Shkalikov
published in: Mathematical Notes
publication date: 2022-01-11T00:00:00Z
review text: The authors study the completeness property of the root functions of the spectral problem \begin{align*} & {{\left( \begin{matrix} {{y}_{1}} \\ {{y}_{2}} \\ \end{matrix} \right)}^{\prime }}-\left( \begin{matrix} p & q \\ r & s \\ \end{matrix} \right)\left( \begin{matrix} {{y}_{1}} \\ {{y}_{2}} \\ \end{matrix} \right)=\lambda \left( \begin{matrix} g & 0 \\ 0 & -h \\ \end{matrix} \right)\left( \begin{matrix} {{y}_{1}} \\ {{y}_{2}} \\ \end{matrix} \right),\,\,\,\,\,\,\,\,\,x\in [0,1], \\ & {{y}_{1}}\left( 0 \right)=0,\,\,\,\,\,\,\,{{y}_{2}}\left( 1 \right)=0. \\ \end{align*} Here $\lambda$ is a spectral parameter, both functions g and h are positive, and the functions $p, q, r$, and s are complex-valued. It is only assumed that all these functions are integrable on the segment $[0, 1]$.
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34L10
zbMATH DE Number: 7455577
zbMATH Keywords: asymptotics of solutions of systems of ordinary differential equations, regular boundary value problems, problems on the completeness of eigenfunctions.
Wikidata QID: Q115253632
MaRDI profile type: Publication
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full work available at URL: s0001434621110353
OpenAlex ID: W4200229432
description: scientific article; zbMATH DE number 7455577