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
Description
Spectral problem for a family of periodic Sturm--Liouville problems \[ u''+λ^2(a(x)-a)u=0 \] 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.
25 pages, 2 figures
25 pages, 2 figures