We study the existence of multiple positive solutions to the two point boundary value problem
-u″(x) = ⋋f(u(x)); O< x < 1 u(0) = 0 = u(1) + αu′(1),
where ⋋ > 0, α > 0. Here f is a smooth function such that f > 0 on [0, r) for some 0 < r ≤ ∞. In particular, we consider the case when f is initially convex and then concave. We discuss sufficient conditions for the existence of at least three positive solutions for a certain range (independent of α) of λ. We apply our results to the nonlinearity which arises in combustion theory and to the nonlinearity (fixed), , which arises in chemical reactor theory.