Affiliation:
1. Department of Mathematics, Penn State University, University Park, PA 16802, USA
Abstract
We consider the Cauchy problem for an ordinary differential equation with discontinuous right-hand side in an L∞ space. Under the assumptions that the vector field is directionally continuous with bounded directional variation, we prove that the O.D.E. has a unique Carathéodory solution, which depends Lipschitz continuously on the data.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Analysis
Reference7 articles.
1. Unique solutions for a class of discontinuous differential equations
2. A. Bressan and W. Shen, Differential Inclusions and Optimal Control, Lecture Notes in Nonlinear Analysis 2, eds. J. Andres, L. Gorniewicz and P. Nistri (Julius Schauder Center for Nonlinear Studies, 1998) pp. 73–87.
3. Differential Equations with Discontinuous Righthand Sides
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献