I'm taking a first course on ODE and i've been asked to provide an example of an IVP which checks the local uniqueness property but does not check the global uniqueness property. My question is about the difference between the two types of uniqueness and on what occasions an IVP has one kind of uniqueness or another. On the other hand , what kind of uniqueness is offered by Picard-Lindelöf theorem?
Any help is useful!