Green's formula

**pdnhan** · May 27th 2011, 04:20 AM

Consider, in any dimension, the PDE:

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

with boundary conditions on $\partial D$ of

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

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

Please help

**girdav** · May 29th 2011, 08:07 AM

What are $p$ , $q$ , $r$ and $\alpha_1$ ?

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