EDIT: could I use a method like that on page 74 of this book? http://paguirre.mat.utfsm.cl/edo-2015-2/perko.pdf It looks like it assumes the Lipshitz constant from a lemma....
I am trying to find a rigorous proof that shows existence and uniqueness of an ode IVP without a Lipschitz condition.
I would prefer a link to a good proof if possible.
I have been looking, but all I can find are the Picard theorem and other theorems that require a Lipschitz constant to show the uniqueness part (but I don't have that in the question I am studying). I have read that the Lipschitz is sufficient but not necessary.
I was looking at the existence theorem for a bit, but I really want something that shows uniqueness as well without the need for the Lipschitz constant.
Here are two variations of my general question...
Thank you for the help.