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Nonexistence of radial solutions of two elliptic boundary value problems

Published online by Cambridge University Press:  14 November 2011

Rafael Ortega
Rafael Ortega
Affiliation:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
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Synopsis

We consider two boundary value problems (of Neumann or related type) associated with the equation in Ω. The existence of a solution was previously established assuming that p < N/(N −s2). (N dimension of Ω.) We prove that this exponent is critical for these problems, at least in the radially symmetric case when Ω is a ball. This is understood in the sense that the existence result does not hold when p ≧ N/(N − 2).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 1-2 , 1990 , pp. 27 - 31
Copyright
Copyright © Royal Society of Edinburgh 1990

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