Two-Point Boundary Value Problems for Ordinary Differential Equations, Uniqueness Implies Existence
Proceedings of the American Mathematical Society
We consider a family of two-point n−1,1 boundary value problems for nth order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions that imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of n−point boundary value problems. Here, we shall replace that standard hypothesis with one in which we assume uniqueness of solutions of a large family of two-point boundary value problems. We then obtain readily verifiable conditions on the nonlinear term that in fact imply the uniqueness of solutions of the large family of two-point boundary value problems.
Online: 1088-6826; print: 0002-9939
American Mathematical Society
Eloe, Paul W. and Henderson, Johnny, "Two-Point Boundary Value Problems for Ordinary Differential Equations, Uniqueness Implies Existence" (2020). Mathematics Faculty Publications. 210.