Uniqueness theorem for ordinary differential equations with Hölder continuity
Pacific Journal of Mathematics
We establish some uniqueness results near 0 for ordinary differential equations of the type u (n) (t) = f(u(t)) which satisfies u(0) = u 0 (0) = · · · = u (m−1)(0) = 0 and u (m) (0) 6= 0 with m ≥ n. We also show that although f is not Lipschitz near 0, it is always Holder ¨ continuous.
Yifei Pan, Mei Wang, and Yu Yan (2012).
Uniqueness theorem for ordinary differential equations with Hölder continuity. Pacific Journal of Mathematics.263 (no. 2), 2228–2244.