Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50017896" target="_blank" >RIV/62690094:18470/21:50017896 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10958-020-05148-7" target="_blank" >https://link.springer.com/article/10.1007/s10958-020-05148-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10958-020-05148-7" target="_blank" >10.1007/s10958-020-05148-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf

Popis výsledku v původním jazyce

In this paper, we consider the operator sheaf − Δ + V+ εℒ ε(λ) + λ2 in the space L2(ℝ2), where the real-valued potential V depends only on the first variable x1, ε is a small positive parameter, λ is the spectral parameter, ℒ ε(λ) is a localized operator bounded with respect to the Laplacian −Δ, and the essential spectrum of this operator is independent of ε and contains certain critical points defined as isolated eigenvalues of the operator −d2dx12+V(x1) in L2(ℝ). The basic result obtained in this paper states that for small values of ε, in neighborhoods of critical points mentioned, isolated eigenvalues of the sheaf considered arise. Sufficient conditions for the existence or absence of such eigenvalues are obtained. The number of arising eigenvalues is determined, and in the case where they exist, the first terms of their asymptotic expansions are found. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Název v anglickém jazyce

Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf

Popis výsledku anglicky

In this paper, we consider the operator sheaf − Δ + V+ εℒ ε(λ) + λ2 in the space L2(ℝ2), where the real-valued potential V depends only on the first variable x1, ε is a small positive parameter, λ is the spectral parameter, ℒ ε(λ) is a localized operator bounded with respect to the Laplacian −Δ, and the essential spectrum of this operator is independent of ε and contains certain critical points defined as isolated eigenvalues of the operator −d2dx12+V(x1) in L2(ℝ). The basic result obtained in this paper states that for small values of ε, in neighborhoods of critical points mentioned, isolated eigenvalues of the sheaf considered arise. Sufficient conditions for the existence or absence of such eigenvalues are obtained. The number of arising eigenvalues is determined, and in the case where they exist, the first terms of their asymptotic expansions are found. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of mathematical sciences

ISSN

1072-3374

e-ISSN

—

Svazek periodika

252

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

135-146

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85096397232