Multiplicity and Stability of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

In this manuscript, we consider a fourth-order three-point boundary value problem. Although the corresponding Green’s function changes its sign on the square of its definition, we obtain the existence of positive and decreasing solutions under some suitable conditions. The arguments are based on the classical Krasosel’skii’s fixed point theorem in cones. Then using Avery–Henderson two fixed point theorem, we obtain multiplicity results. In the end, we establish some conditions under which the solutions of the considered problem are generalized Ulam–Hyers stable. Some examples are given to illustrate our main results.