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


Erkut M. H. , Borisenok S. , Caglar M., Polatoglu Y.

JOURNAL OF DIFFERENTIAL EQUATIONS, vol.251, no.12, pp.3403-3420, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 251 Issue: 12
  • Publication Date: 2011
  • Doi Number: 10.1016/j.jde.2011.08.023
  • Title of Journal : JOURNAL OF DIFFERENTIAL EQUATIONS
  • Page Numbers: pp.3403-3420

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.