Uniqueness of positive solutions for a class of ODE's with Dirichlet boundary conditions

Abstract

We study the uniqueness of positive solutions of the boundary-value problem u'' + α(t)u' + ƒ(t, u) = 0, t ∈ (0, b) u(0) = 0 = 0, u(b) = 0, where 0 < b < ∞, α ∈ C1[0, ∞) and ƒ ∈ C1([0, ∞) x [0, ∞), [0, ∞)) satisfy suitable conditions. The proof of our main result is based on the shooting method and the Sturm comparison theorem.