On the existence of strong solutions to autonomous differential equations with minimal regularity
- 作者：Charlie H. Cooke
- 关键词：Strong and weak solutions of an ordinary differential equation ; Autonomous differential equation ; Global orbit ; Semi-orbit
- 刊名：Applied Mathematics Letters
- 出版年：2007
- 期刊代码：5_08939659
- 类别：mt
- 出版时间：February 2007
- 卷：20
- 期：2
- 页码：213-215
- 文件大小：111 K
摘要
For proving the existence and uniqueness of strong solutions to
the most quoted condition seen in elementary differential equations texts is that F(Y) and its first derivative be continuous. One wonders about the existence of a minimal regularity condition which allows unique strong solutions. In this note, a bizarre example is seen where F(Y) is not differentiable at an equilibrium solution; yet unique non-global strong solutions exist at each point, whereas global non-unique weak solutions are allowed. A characterizing theorem is obtained.