I am looking for an easy but rigorous reference for FEM methods for non linear PDEs like the p-laplace equattion or non linear heat equation ect.
Can one recommend me a good exposition of this topic please.
Questions I have in mind is, where do I know that the resulting system of non linear equations is uniquely solvable or when to choose what basis functions and what are pros and cons of different basis functions ect.
I literally cant find something about that on the internet. I only find papers where they treat non trivial forms of FEM for non linear equations.
Analysis of nonlinear PDEs is very specific to each equation and literature on numerical PDEs is similar. Everything has to be tailored to the specific nature of the equations you are studying. I think papers are your only sure bet if you have something very specific in mind or you want state-of-the-art methods. That being said, Nonlinear Finite Element Methods by Wriggers is quite good, but it necessarily focuses on a few different examples from applications.