Uniqueness Theorems for Ordinary Differential Equations with Hölder Continuity

Abstract

We study ordinary differential equations of the type $u^{(n)}(t)=f(u(t))$ with initial conditions $u(0)=u^{\prime }(0)=...=u^{(m-1)}(0)=0$ and $u^{(m)}(0)\ne 0$ where $m\ge n$, no additional assumption is made on $f$. We establish some uniqueness results and show that $f$ is always Hölder continuous.

To appear in Pacific Journal of Mathematics