Solution and positive solution for a semilinear third-order two-point boundary value problem Original Research Article

In this paper, several existence results of solution and positive solution are obtained for the semilinear third-order two-point boundary value problem μ‴ = ƒ (t, μ, μ″), μ(0) = A, μ(1) = B, μ″(0) = C. The discussion is based on the Leray-Schauder fixed-point theorem and the system of integral equations. The main conditions are local. In other words, the problem may possess a solution or positive solution provided the “height” of nonlinear term ƒ (t, μ, ν) is appropriate on a bounded set of its domain.