Existence results of 2mm-point boundary value problem of Sturm–Liouville type with sign changing nonlinearity

In this paper, we are concerned with a 2m2m-point boundary value problem with one-dimensional pp-Laplacian. By using a fixed point theorem in a cone, the existence of at least one, two or three positive solutions under some sufficient conditions is obtained. The interesting points are that the boundary condition is a new kind of Sturm–Liouville type and the nonlinearity may change sign.