I would like to derive the spherical symmetric solutions (or in another words make use of the fundamental solutions) of the following PDE:
\begin{equation} \Delta u(x)+\lambda u(x)=0, \quad \lambda>0, \quad x\in \mathbb{R} ^2 \end{equation}
I know how to solve for the fundamental solutions of the Laplace equation: \begin{equation} \Delta u(x)=0 \end{equation} but I am not sure how to proceed with the other one. Thank you for your time!