Can someone give me some references to read where existence/uniqueness of nonlinear parabolic PDE are treated via the Galerkin method or fixed point methods or something like that (anything but semigroups, which I am not faimilar with)?


I always come across H. Amann's work when I search on this topic but his work appears a bit complicated to me.



Nonlinear parabolic PDEs existence with Galerkin method?
Well, it is difficult to have something without semigroups, since [Lunardi](http://books.google.de/books/about/Analytic_Semigroups_and_Optimal_Regulari.html?id=mWojiHzg9bEC&redir_esc=y) is still one of the most comprehensive references. 


Try [Krylov](http://www.ams.org/bookstore-getitem/item=gsm-96) then, it is an excellent read. 


If you are fixed on Galerkin, then [Zeidler:](http://books.google.de/books/about/Nonlinear_Functional_Analysis_and_Its_Ap.html?id=MFi9SkoK750C&redir_esc=y) *Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear Monotone Operators* is a good start.


