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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120854Spectral 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 figuresSpectral Theory34B24; 33C15Asymptotic behaviour of the positive spectrum for a family of periodic Sturm-Liouville problems in the transition from a definite problem to indefinite onetext