We will do it in two pieces. Let us recall that whenever we have a linear, inhomogeneous problem, the general solution is given by any particular solution, plus the general solution of the related homogeneous problem. It has no delta function, so its solutions will be completely regular. In other words, the singular parts of any two Green functions for the same equation, but different boundary conditions, will be the same. This last equality is because F is independent of .
B is undetermined.
We may as well choose it to be 0 at this stage. Of course there is no singularity in the constant function, so its derivatives do not contribute to the delta function. See exercise 3 for why the assumption that u is square integrable is necessary. We next discuss a method for finding the Green function on regions other than R n . Model Problem XIX.1 .