Positive Solutions of a Weak Semipositone Third-Order Three-Point Boundary Value Problem

The positive solutions are studied for the nonlinear third-order three-point boundary value problem u (t) = f(t,u(t)), a.e. t ∈ [0,1], u(0) = u (η) = u (1) = 0, where the nonlinear term f(t,u) is a Carathodory function and there exists a nonnegative function h ∈ L1[0,1] such that f(t,u) ≥ -h(t). The existence of n positive solutions is proved by considering the integrations of "height functions" and applying the Krasnosel'skii fixed point theorem on cone.