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

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

arxiv.org/abs/math/0612849v1

Mathematics

Spectral Theory

25 pages, 2 figures

Scientific paper

Spectral problem for a family of periodic Sturm--Liouville problems \[
u''+\lambda^2(a(x)-a)u=0 \] depending on the parameter (a\in\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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