A uniqueness criterion for ordinary differential equations
type: Item
instance of: scholarly article
title: A uniqueness criterion for ordinary differential equations
author: Yanyan Li
published in: Journal of Differential Equations
publication date: 2022-11-11T00:00:00Z
review text: Consider the initial-value problem: \(x^{\prime}(t)=F(t,x(t))\), \(t\in [0,t_0]\), \(x(0)=x_0\). As a main result, the author shows that a convex combination of Nagumo- and Osgood-type growth conditions for the spatial variation of continuous functions ensures the uniqueness of the solution to the initial-value problem and the convergence of the successive approximations, defined by \(x_0 (t)=x_0\), \(t\in[0,T]\), \(x_{n+1} (t)=x_0 + \int_0^t F(s,x_n (s)) ds\), \(n>0\).
reviewed by: Erdoǧan Şen
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 7615167
zbMATH Keywords: initial value problem
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: j.jde.2022.09.035
OpenAlex ID: W4303415454
cites work: Q4274968
cites work: Q3491921
cites work: Fourier Analysis and Nonlinear Partial Differential Equations
cites work: The differential equation x=fox
cites work: Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts
cites work: A note on the uniqueness of solutions of ordinary differential equations
cites work: The trajectories of particles in Stokes waves
cites work: Particle trajectories in extreme Stokes waves
cites work: Particle trajectories in solitary water waves
cites work: Differentiability of functions in the Zygmund class
cites work: A Generalization of the Nagumo Uniqueness Criterion
cites work: Ordinary differential equations.
cites work: Weierstrass functions in Zygmund’s class
cites work: Q4064235
cites work: Lipschitz spaces, smoothness of functions, and approximation theory
cites work: Q5509994
cites work: A uniqueness theorem for ordinary differential equations involving smooth functions
cites work: Some remarks on Nagumo’s theorem
cites work: On the Convergence of Successive Approximations
cites work: Log-Lipschitz regularity and uniqueness of the flow for a field in \((W_{\text{loc}}^{n/p+1,p}(\mathbb{R}^n))^n\)
cites work: Smooth functions
DOI: 10.1016/J.JDE.2022.09.035
description: scientific article; zbMATH DE number 7615167