Spectrum of a linear fourth-order differential operator and its applications

In this paper, we apply the disconjugacy theory and Elias's spectrum theory to study the positivity and the spectrum structure of the linear operator u(4)+Mu coupled with the clamped beam boundary conditions (1.2). We also study the positivity and the spectrum structure of the more general oper...

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Bibliographic Details
Published in:Mathematische Nachrichten Vol. 286; no. 17-18; pp. 1805 - 1819
Main Authors: Ma, Ruyun, Wang, Haiyan, Elsanosi, Mohammed
Format: Journal Article
Language:English
Published: Weinheim Blackwell Publishing Ltd 01.12.2013
Wiley Subscription Services, Inc
Subjects:
34B10
34B18
Clamped beam
disconjugate
Finite element analysis
fourth-order equations
global bifurcation
nodal solutions
ISSN:0025-584X, 1522-2616
Online Access:Get full text
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Summary:In this paper, we apply the disconjugacy theory and Elias's spectrum theory to study the positivity and the spectrum structure of the linear operator u(4)+Mu coupled with the clamped beam boundary conditions (1.2). We also study the positivity and the spectrum structure of the more general operator u(4)+p(t)u coupled with (1.2). As the applications of our results on positivity and spectrum of fourth‐order linear differential operators, we show the existence of nodal solutions for the corresponding nonlinear problems via Rabinowitz's global bifurcation theorem.
Bibliography:istex:CEFC839E5F2558AB0241E4EE7FEF8692A737440A
ArticleID:MANA201200288
ark:/67375/WNG-T43B1P9R-G
MoHDNAJY@Hotmail.com
Haiyan.Wang@asu.edu
e‐mail
Phone: +1 602 543 5635, Fax: +1 602 543 5635
Phone: +86 931 7971413, Fax: +86 931 7971297
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ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201200288