A note on Cauchy-Lipschitz-Picard theorem

Abstract

Abstract In this note, we try to generalize the classical Cauchy-Lipschitz-Picard theorem on the global existence and uniqueness for the Cauchy initial value problem of the ordinary differential equation with global Lipschitz condition, and we try to weaken the global Lipschitz condition. We can also get the global existence and uniqueness.

Keywords

• initial value problems
• generalized Lipschitz condition
• global existence and uniqueness