A Two-Point Boundary Value Problem
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.
Unable to display preview. Download preview PDF.