# Green's Equation for $\Delta u=0$ with specified conditions.

I need to find the Green's function for $$\Delta u=0$$ in the upper half plane subject to $$G(x,0;x_0,y_0)=0=\lim_{y\rightarrow\infty} G.$$ I know that $$\Delta G=0$$ and I have tried solving this with the free-space Greens and by setting it up and solving for $$G$$ with separation of variables. None of my work goes anywhere.