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

Ruyun Ma, Haiyan Wang, Mohammed Elsanosi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1805-1819
Number of pages15
JournalMathematische Nachrichten
Volume286
Issue number17-18
DOIs
StatePublished - Dec 1 2013

Keywords

  • Clamped beam
  • Disconjugate
  • Fourth-order equations
  • Global bifurcation
  • Nodal solutions

ASJC Scopus subject areas

  • Mathematics(all)

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