Limit-point and limit-circle criteria for Sturm-Liouville equations with intermittently negative principal coefficients

Abstract

SynopsisLimit-point and limit-circle criteria are given for the generalised Sturm-Liouville differential expressionwhere(i)p, q, andware real-valued on[a, b),(ii)p−1, q, ware locally Lebesgue integrable on[a, b),(iii)w> 0 almost everywhere on[a, b)and the principal coefficientpis allowed toassume both positive and negative values.