Optimal version of the Picard–Lindelöf theorem

Abstract

Consider the differential equation $y'=F(x,y)$. 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.

Keywords

• ordinary differential equations
• picard–lindelöf theorem
• global existence
• uniqueness