Vol. 263, No. 2, 2013

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Uniqueness theorem for ordinary differential equations with Hölder continuity

Yifei Pan, Mei Wang and Yu Yan

Vol. 263 (2013), No. 2, 453–473
Abstract

We study ordinary differential equations of the type u(n)(t) = f(u(t)), with initial conditions u(0) = u(0) = = u(m1)(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.

Keywords
uniqueness of solutions, ordinary differential equations
Mathematical Subject Classification 2010
Primary: 34A12
Milestones
Received: 25 January 2012
Revised: 20 February 2012
Accepted: 7 March 2012
Published: 31 May 2013
Authors
Yifei Pan
Department of Mathematical Sciences
Indiana University–Purdue University Fort Wayne
Fort Wayne, IN 46805
United States
School of Mathematics and Informatics
Jiangxi Normal University
Nanchang
China
Mei Wang
Department of Statistics
University of Chicago
Chicago, IL 60637
United States
Yu Yan
Department of Mathematics and Computer Science
Huntington University
Huntington, IN 46750
United States