I need a maximum principle that says:
If $L$ is an elliptic operator and $u$ is a positive function ($u\in C^2(\Omega)$, with $\Omega\subset\mathbb{R}^n$ an unbounded domain) such that $Lu\geq0$ in $\Omega$ and $\limsup_{|x| \to \infty} u\leq0$, then $u\leq0$ in $\Omega$.
If you know a maximum principle like that, please tell me the book or text.
Thank you!