I am wondering if it is possible to solve the following equation:
$$\nabla^2\nabla^2 u(\xi,\eta)+u(\xi, \eta) = \delta(\xi)$$
with $\nabla^2=\frac{2}{a^2 \,(\mathrm{cosh}(\xi)-\,cos(\eta))} \, \left(\frac{\partial^2}{\partial\xi^2}+\frac{\partial^2}{\partial\eta^2}\right)$ the Laplace operator in elliptical coordinates, $\xi \in[0,\infty]$ and $\eta \in [0,2\pi]$, and $\delta$ the Dirac delta function.
Is there something similar to the Hankel transform for polar coordinates in case of elliptical coordinates? Thank you.