Spectral estimates for a nonhomogeneous difference problem

A. Kristály, Mihai Mihǎilescu, Vicenţiu Rǎdulescu, Stepan Tersian

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.

Original languageEnglish
Pages (from-to)1015-1029
Number of pages15
JournalCommunications in Contemporary Mathematics
Volume12
Issue number6
DOIs
Publication statusPublished - Dec 2010

Fingerprint

Difference equations
Eigenvalue
Estimate
Difference equation
Eigenvalue Problem
Framework

Keywords

  • continuous spectrum
  • critical point
  • discrete boundary value problem
  • Eigenvalue problem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Spectral estimates for a nonhomogeneous difference problem. / Kristály, A.; Mihǎilescu, Mihai; Rǎdulescu, Vicenţiu; Tersian, Stepan.

In: Communications in Contemporary Mathematics, Vol. 12, No. 6, 12.2010, p. 1015-1029.

Research output: Contribution to journalArticle

Kristály, A. ; Mihǎilescu, Mihai ; Rǎdulescu, Vicenţiu ; Tersian, Stepan. / Spectral estimates for a nonhomogeneous difference problem. In: Communications in Contemporary Mathematics. 2010 ; Vol. 12, No. 6. pp. 1015-1029.
@article{3bc26761476e4dd19d704497b3c28d26,
title = "Spectral estimates for a nonhomogeneous difference problem",
abstract = "We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.",
keywords = "continuous spectrum, critical point, discrete boundary value problem, Eigenvalue problem",
author = "A. Krist{\'a}ly and Mihai Mihǎilescu and Vicenţiu Rǎdulescu and Stepan Tersian",
year = "2010",
month = "12",
doi = "10.1142/S0219199710004093",
language = "English",
volume = "12",
pages = "1015--1029",
journal = "Communications in Contemporary Mathematics",
issn = "0219-1997",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "6",

}

TY - JOUR

T1 - Spectral estimates for a nonhomogeneous difference problem

AU - Kristály, A.

AU - Mihǎilescu, Mihai

AU - Rǎdulescu, Vicenţiu

AU - Tersian, Stepan

PY - 2010/12

Y1 - 2010/12

N2 - We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.

AB - We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.

KW - continuous spectrum

KW - critical point

KW - discrete boundary value problem

KW - Eigenvalue problem

UR - http://www.scopus.com/inward/record.url?scp=78650720294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650720294&partnerID=8YFLogxK

U2 - 10.1142/S0219199710004093

DO - 10.1142/S0219199710004093

M3 - Article

AN - SCOPUS:78650720294

VL - 12

SP - 1015

EP - 1029

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

IS - 6

ER -