Resonant singular boundary value problems

Abstract

Existence theory is developed for the ''resonant'' singular problem (1/(pq))(py')' + lambda(0)y = f(t,y,py') almost everywhere on [0, 1] with lim(t-->0+) p(t)y'(t) = ay(1) + blim(t-->1-) p(t)y'(t) = 0. Here lambda(0) is the first eigenvalue of (1/(pq))(pu')' + lambda u = 0 almost everywhere on [0,1] with lim(t-->0+) p(t)u'(t) = au(1) + blim(t-->1-) p(t)u'(t) = 0. We do not assume integral(0)(1) ds/p(s) < infinity in this paper.