Applied Mathematics Letters
For proving the existence and uniqueness of strong solutions to
dY/dt = F(Y), Y(0) = C,
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.
Original Publication Citation
Cooke, C. H. (2007). On the existence of strong solutions to autonomous differential equations with minimal regularity. Applied Mathematics Letters, 20(2), 213-215. doi:10.1016/j.aml.2006.02.031
Cooke, Charlie H., "On the Existence of Strong Solutions to Autonomous Differential Equations with Minimal Regularity" (2006). Mathematics & Statistics Faculty Publications. 82.