Continuity and nodal properties near infinity for solutions of 2- dimensional Schrödinger equations (Q1080058)

The authors consider the Schrödinger equation: \[ (-\Delta +V-E)\psi =0\quad in\quad \Omega_ R=\{x\in {\mathbb{R}}^ 2:\quad | x| \geq R\} \] with Dirichlet condition on the boundary of \(\Omega_ R\). They study continuity properties of \(\psi\) and the nodal domains defined by \(\psi\) under suitable assumptions on V.