Solution To N-Dimensional Sturm-Liouville-Like Equations Using Multi-Dimensional Schwarzian

Abstract

In the present work we produce the solution to the n-dimensional Sturm-Liouville-like equations in R(n). 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 Mobius transformations defined in R(n) correspond to a straightforward generalization of those of the one-dimensional Schwarzian. (C) 2011 Elsevier Inc. All rights reserved.