$\Omega$ is a bounded open subset of $R^n$ $$ -\Delta u -u\ln u=\lambda u \\ u|_{\partial\Omega}=0 $$
What should I read about this eigenvalue question ? I mean some reference or book.I want to answer this eigenvalue question as my homework.
At the beginning, I want to use the fix point theory, but if let $Lu=\frac{-\Delta u -u\ln u}{\lambda}$, I don't know what the $L$ maps suitable space (for example $H_0^2(\Omega)$) to. In fact ,about this question I have asked a question.
Today I read a connected question, but I am unfamiliar with the energy method and don't understand the answer of it. If this is a suitable way for my question, I should read which chapters of Evans' PDE or other books?
I really don't know whether suitable my question is .I just a beginner of PDE. If there are any doubt , please tell me .thanks.