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On finite Morse index solutions of two equations with negative exponent

Published online by Cambridge University Press:  30 January 2013

Juan Dávila  and
Dong Ye
Juan Dávila
Affiliation:
Departamento de Ingenierίa Matemática and CMM (UMI 2807 CNRS), Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile (jdavila@dim.uchile.cl)
Dong Ye
Affiliation:
Département de Mathématiques, UMR 7122, Université de Lorraine, site Metz, Ile de Saulcy, 57045 Metz, France (dong.ye@univ-metz.fr)
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Abstract

We consider the following equations involving negative exponent:

where p > 0. Under optimal conditions on the parameters α > −2 and p > 0, we prove the non-existence of finite Morse index solution on exterior domains or near the origin. We also prove an optimal regularity result for solutions with finite Morse index and isolated rupture at 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 1 , February 2013 , pp. 121 - 128
Copyright
Copyright © Royal Society of Edinburgh 2013

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