Optimal version of the Picard-Lindelöf theorem - Schlage-Puchta Jan-Christoph (Electronic journal of qualitative theory of differential equations, 2021)
Consider the differential equation y 0 = F(x, y). We determine the weakest possible upper bound on |F(x, y) − F(x, z)| which guarantees that this equation has for all initial values a unique solution, which exists globally.