Asymptotic behaviour of the positive spectrum for a family of periodic Sturm-Liouville problems in the transition from a definite problem to indefinite one

2006/12/29 by D. A. Popov, Popov, D. A.
Mathematics · #33C15 #34B24 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:33C15 #msc:34B24

paper · pdf · doi:10.48550/arxiv.math/0612849

25 pages, 2 figures

arxiv created 2006/12/29 · arxiv updated 2009/12/01

Abstract

Spectral problem for a family of periodic Sturm--Liouville problems u''+λ²(a(x)-a)u=0 depending on the parameter (a∈\mathbb R) is considered. An interpolation formula describing the behaviour of the branches of the spectrum in the transition from a definite problem to indefinite one is obtained.

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