Uniqueness Theorems for Ordinary Differential Equations with Hölder Continuity

2012/09/26 by Yifei Pan, Mei Wang, Pan, Yifei +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1209.6064

openalex publication_date 2012/09/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study ordinary differential equations of the type u⁽ⁿ⁾(t)=f(u(t)) with initial conditions u(0) = u'(0) =... = u^(m-1)(0) = 0 and u^(m)(0) ≠ 0 where m ≥ n, no additional assumption is made on f. We establish some uniqueness results and show that f is always Hölder continuous.

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