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Spectrum of a linear fourth‐order differential operator and its applications
Author(s) -
Ma Ruyun,
Wang Haiyan,
Elsanosi Mohammed
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200288
Subject(s) - mathematics , spectrum (functional analysis) , differential operator , operator (biology) , linear map , operator theory , mathematical analysis , nonlinear system , boundary value problem , order (exchange) , bifurcation , semi elliptic operator , pure mathematics , finance , repressor , quantum mechanics , transcription factor , economics , gene , biochemistry , chemistry , physics
In this paper, we apply the disconjugacy theory and Elias's spectrum theory to study the positivity and the spectrum structure of the linear operatoru ( 4 ) + M u coupled with the clamped beam boundary conditions (1.2). We also study the positivity and the spectrum structure of the more general operatoru ( 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.