Resonances for Euler–Bernoulli operator on the half-line

Результат исследований: Научные публикации в периодических изданияхстатья

3 Цитирования (Scopus)

Выдержка

We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.

Язык оригиналаанглийский
Страницы (с-по)534-566
Число страниц33
ЖурналJournal of Differential Equations
Том263
Номер выпуска1
DOI
СостояниеОпубликовано - 5 июл 2017

Отпечаток

Half line
Operator
Coefficient
Counting Function
Trace Formula
Fourth Order
Differential operator
Radius
Eigenvalue
Interval

Предметные области Scopus

  • Анализ

Цитировать

@article{dcc9faca99e641be99320dd704d37ad2,
title = "Resonances for Euler–Bernoulli operator on the half-line",
abstract = "We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.",
keywords = "Fourth order operators, Resonances, Scattering",
author = "Andrey Badanin and Korotyaev, {Evgeny L.}",
year = "2017",
month = "7",
day = "5",
doi = "10.1016/j.jde.2017.02.041",
language = "English",
volume = "263",
pages = "534--566",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Elsevier",
number = "1",

}

Resonances for Euler–Bernoulli operator on the half-line. / Badanin, Andrey; Korotyaev, Evgeny L.

В: Journal of Differential Equations, Том 263, № 1, 05.07.2017, стр. 534-566.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Resonances for Euler–Bernoulli operator on the half-line

AU - Badanin, Andrey

AU - Korotyaev, Evgeny L.

PY - 2017/7/5

Y1 - 2017/7/5

N2 - We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.

AB - We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.

KW - Fourth order operators

KW - Resonances

KW - Scattering

UR - http://www.scopus.com/inward/record.url?scp=85014543170&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2017.02.041

DO - 10.1016/j.jde.2017.02.041

M3 - Article

AN - SCOPUS:85014543170

VL - 263

SP - 534

EP - 566

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -