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Solution to n-dimensional Sturm-Liouville-like equations using multi-dimensional Schwarzian |
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| Authors: | MH Erkut M Ça?lar |
| Affiliation: | a Department of Physics, ?stanbul Kültür University, Bak?rköy 34156, ?stanbul, Turkey b Abdus Salam School of Mathematical Sciences, Government College University, 68-B New Muslim Town, 54600 Lahore, Pakistan c Department of Mathematics and Computer Science, ?stanbul Kültür University, Bak?rköy 34156, ?stanbul, Turkey |
| Abstract: | 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. |
| Keywords: | Partial differential equations Schwarzian derivative |
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