In mathematics, a uniqueness theorem is a theorem proving that certain conditions determine a unique solution. Examples of uniqueness theorems include:

https://en.wikipedia.org/wiki/Uniqueness_theorem

I know the uniqueness theorem, i look for some uniqueness theorem of PDE !

Dear Behrad, there are not general existence and uniqueness theorems for nonlinear PDE problems; usually, if there is a global (= on all the PDE domain) E-U theorem for linear case, there is a local E-U theorem for nonlinear case (Signorini methods of sequential approximations).

Gianluca

I dont look for general existence theorem, any sufficient or locally existance is allright.

Helo, I am also looking for some tex. I know there exist a uniqueness and existence theorem for systems of first order PDE

There are some basic existence and uniqueness for PDE that can be explained from the Arzela Ascolis theorem