Solution to n-dimensional Sturm–Liouville-like equations using multi-dimensional Schwarzian

In the present work we produce the solution to the n-dimensional Sturm–Liouville-like equations in Rn. To make it, we define the multi-dimensional Schwarzian derivative of a real-valued function of n variables and show that its basic properties related to its invariance under the action of a group of multi-dimensional Möbius transformations defined in Rn correspond to a straightforward generalization of those of the one-dimensional Schwarzian.