Consider, in any dimension, the PDE:

$\displaystyle \nabla \cdot (p \nabla v) + qv +\lambda rv = 0 $ $\displaystyle in$ $\displaystyle D$

with boundary conditions on $\displaystyle \partial D$ of

$\displaystyle \alpha _{1}v +\frac{\partial v}{\partial n} =0$ where $\displaystyle n$ is the normal direction.

Use Green's formula to prove that there cannot be any generalized eigenfunctions: such generalized eigenfunctions $\displaystyle w$ are defined as satisfying $\displaystyle Lw +\lambda rw = rv$ and the same boundary conditions.

Please help