Nonlinear interpolation and boundary value problems This book is devoted to the study of solutions of nonlinear ODE boundary value problems as nonlinear interpolation problems. In 1967 Lasota and Opial showed that under suitable hypotheses if solutions of a second order nonlinear differential equation passing through two distinct points are unique when they exist then in fact a solution passing through two distinct points does exist. That result coupled with the pioneering work of Philip Hartman on what was then called unrestricted n parameter families has stimulated 50 years of rapid development in the study of solutions of boundary value problems as nonlinear interpolation problems. The purpose of this book is two fold. First the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well defined area of study in the qualitative theory of ordinary differential equations. Second methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation Uniqueness implies uniqueness Uniqueness implies existence Nonlocal boundary value problems: uniqueness and existence Boundary value problems for finite difference equations Boundary value problems for dynamic equations on time scales