Multiple Solutions to a Third-Order Three-Point Nonhomogeneous Boundary Value Problem Aided by Nonlinear Programming Methods

In this work, we consider a third order equation of three points with non homogeneous conditions at the border. We apply Avery Peterson's theorem, and present a theoretical result that guarantees the existence of multiple solutions to this problem under certain conditions. In addition, we present non-trivial examples and a new numerical method based on optimization is introduced.