A Two-Point Boundary Value Problem

Abstract

For the purpose of preparing for the treatment of boundary value problems for elliptic partial differential equations we consider here a simple two-point boundary value problem for a second order linear ordinary differential equation. In the first section we derive a maximum principle for this problem, and use it to show uniqueness and continuous dependence on data. In the second section we construct a Green’s function in a special case and show how this implies the existence of a solution. In the third section we write the problem in variational form, and use this together with simple tools from functional analysis to prove existence, uniqueness, and continuous dependence on data.