On the paper: Decay of Solutions to Nonlinear Schrodinger Equations.
Let $u$ be a solution of the equation $$Hu+|u|^2u=0,$$ where $H$ is a Schrodinger operator, i.e. $-\Delta+V$ and $V$ is a (smooth)function with bounded point--wise norm.
Let $W(u)=|u|^2$, if $u\in L^2(\mathbb R^n),~n\geq3$ and $u\to 0$ as $|x|\to \infty$.
Q: How to show that $W $ is relative-compact w.r.t. $H$?
PS: I see such a result on paper : Decay of Solutions to Nonlinear Schrodinger Equations, Proc. Amer. Math. Soc. 136 (2008), 2565-2570.
The author gave a reference, (Chapter 8) A. Pankov, Lecture Notes on Schr¨odinger Equations, Nova Publ., 2007. but I can not find it online or on campus library.
