Direct and inverse sturm-liouville problems on finite intervals

Abstract

Consider Eq. (2.1) on the interval (0, π). If originally the equation is considered on another finite interval (a, b), then by a simple change of the independent variable (Formula Presented) it can always be transferred to (0, π). Let q be a real-valued function, (Formula Presented) and h, H be real numbers. Together with the equation (Formula Presented) consider the homogeneous boundary conditions (Formula Presented) There exists an infinite sequence of real numbers {λn}n=0∞ such that λn < λm if n < m, λn → +∞ when n →∞, and for every λn the equation (Formula Presented) admits a nontrivial solution yn satisfying the conditions (3.2).