Sturm–Liouville problems with eigenparameter dependent boundary conditions

Abstract

Sturm theory is extended to the equation for 1/ p , q , r ∈ L 1 [0, 1] with p, r > 0, subject to boundary conditions and Oscillation and comparison results are given, and asymptotic estimates are developed. Interlacing of eigenvalues with those of a standard Sturm–Liouville problem where the boundary conditions are a j y ( j ) = c j ( py ′)( j ), j =0, 1, forms a key tool.