On the existence of strong solutions to autonomous differential equations with minimal regularity Original Research Article

For proving the existence and uniqueness of strong solutions to equation(1) View the MathML sourcedYdt=F(Y),Y(0)=C, Turn MathJax on the most quoted condition seen in elementary differential equations texts is that F(Y)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)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.