Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter. I

Abstract

We consider the Sturm-Liouville equation -y″ + qy = λy on [0, 1], subject to the boundary conditions y(0) cos α = y′(0) sin α, α ∈ [0, π), and y′/y (1) = aλ + b - ∑k=1nbk/λ - ck. Topics treated include existence and asymptotics of eigenvalues, oscillation of eigenfunctions, and transformations between such problems.