Strongly singular Sturm-Liouville problems

We consider a Sturm- Liouville operator Lu = - (r(t)u ')' + p(t)u, where r is a (strictly) positive continuous function on ]a, b[ and p is locally int egrable on ]a, b[. Let r(1)(t) = integral (t)(a)(1/r) ds and choose any c i s an element of ]a, b[. We are interested in the eigenvalue problem Lu = la mbdam(t)u, u(a) = u(b) = 0, and the corresponding maximal and anti-maximal principles, in the situation when 1/r is an element of L-1(a, c), 1/r is no t an element of L-1(c, b), pr(1) is not an element of L-1 (a, c) and pr(1) is not an element of L-1(c, b).