A Nagumo-like uniqueness result for a second order ODE

TL;DR

This paper extends Nagumo-like uniqueness criteria from first order to second order nonlinear ODEs, providing a new theoretical result that broadens the understanding of solution uniqueness in differential equations.

Contribution

It introduces a novel extension of Nagumo's uniqueness theorem to second order nonlinear ODEs, filling a gap in the existing mathematical theory.

Findings

Established a Nagumo-like uniqueness criterion for second order ODEs

Generalized previous first order results to higher order equations

Provides a theoretical foundation for solution uniqueness in nonlinear second order ODEs

Abstract

In this note, we present an extension to second order nonlinear ordinary differential equations (ODEs) of the Nagumo-like uniqueness criterion for first order ODEs established in [A. Constantin, On Nagumo's theorem, Proc. Japan Acad. 86(A) (2010), pp. 41--44].