Resonances for Euler–Bernoulli operator on the half-line

Research outputpeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)534-566
Number of pages33
JournalJournal of Differential Equations
Volume263
Issue number1
DOIs
Publication statusPublished - 5 Jul 2017

Scopus subject areas

  • Analysis

Cite this

@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",

}

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

VL - 263

SP - 534

EP - 566

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -