# Green's Function Solutions

So, I'm considering a PDE and trying to solve for its green function first. To this end, I solve the following helmholtz equation:

$$\frac{d^2g}{dx^2}+\frac{d^2g}{dy^2}+\frac{d^2g}{dz^2}-\alpha^2g=\delta(x-\xi)\delta{(y-\eta)}\delta{(z-\rho)}$$

Well, I can solve this PDE for g, but what happens to the solution when $x=\xi$,$y=\eta$, etc? In that case, would the green's function fail to solve the PDE? So, it fails to solve the homogeneous case at the "separation point"? Just trying to understand what happens at this odd location.

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