How to solve the screened poisson Equation in 2D?

[allyouneedispop]

Hi,

I am trying hard to solve the screened poisson equation in 2D for u(x,y):

 

\nabla^2 u(x,y) - u(x,y) =f(x,y) with f(x,y)=exp(-(x^2+y^2)) and

u(x,y)=0 for x,y -> infinity.

 

Could anybody know what is the analytical solution of this equation?

 

I would really thank who could give me any clue about it.