A bifurcation result for Sturm-Liouville problems with a set-valued term.
The aim of this article is to present a simple proof of the theorem about perturbation of the Sturm-Liouville operator in Liouville normal form.
We study a Sturm-Liouville problem containing a spectral parameter in the boundary conditions. We associate to this problem a self-adjoint operator in a Pontryagin space Π₁. Using this operator-theoretic formulation and analytic methods, we study the asymptotic behavior of the eigenvalues under the variation of a large physical parameter in the boundary conditions. The spectral analysis is applied to investigate the well-posedness and stability of the wave equation of a string.