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