Asymptotic behaviour of the positive spectrum for a family of periodic Sturm-Liouville problems in the transition from a definite problem to indefinite one
Abstract
Spectral problem for a family of periodic Sturm--Liouville problems \[ u''+λ2(a(x)-a)u=0 \] depending on the parameter (a∈ 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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