Consider a function $f$ that satisfies the following differential equation:
\begin{equation} \Delta f - \lambda^2 ((\Delta f)^2) = 0, \end{equation}
where $\lambda$ is some real constant. Expressing $\Delta$ in spherical coordinates, does the differential equation admit separable solutions of the type $f(r,\theta,\phi) = R(r)\Theta(\theta)\Phi(\phi)$ or does this only makes sense if $\lambda = 0$?