A second-order singular boundary value problem

We study the second-order boundary value problem −″(t) = α(t)f(u(t)), o < t < 1, satisfying αu(0) − βu″(0) = 0, γu(1) + δu″(1) = 0, where a(t) = Πi=1n ai(t) and α, β, γ, δ ≥ 0, αγ + αδ + βγ > 0. We assume that each ai(t) ε LPi [0, 1] for pi ≥ 1 and that each ai(t) has a singularity in (0, 1). To show the existence of countably many positive solutions, we apply Hölderʹs inequality and Krasnoselʹski ʹs fixed-point theorem for operators on a cone.