A multiplicity result for a boundary value problem with infinitely many singularities

We consider the second order boundary value problem −u (t ) = a(t)f (u(t)), 0 < t <1, u(0) = u(1) = 0, where a(t) ∈ Lp[0, 1] for some p 1 and has countably many singularities in [0, 1/2). We show that there exist countably many positive solutions using Hölder’s inequality and Krasnosel’ski˘ı’s fixed point theorem for operators on a cone.  2002 Elsevier Science (USA). All rights reserved.