Positive Solutions of a Third-Order Three-Point BVP with Sign-Changing Green’s Function

Abstract EN

We are concerned with the following third-order three-point boundary value problem: u ′ ′ ′ t = f t , u t , t ∈ 0 , 1 , u ′ 0 = u 1 = 0 and u ′ ′ η - α u ′ 1 = 0 , where α ∈ 0 , 1 and η ∈ ( 14 + α ) / ( 24 - 3 α ) , 1 .

Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson.