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Existence and non-existence results for semilinear elliptic problems in unbounded domains

Published online by Cambridge University Press:  14 November 2011

M. J. Esteban  and
P. L. Lions
M. J. Esteban
Affiliation:
Laboratoire d'Analyse Numérique, Université P. et M. Curie, 4 Place Jussieu, 75230 Paris Cedex, France
P. L. Lions
Affiliation:
C.N.R.S. Laboratoire d'Analyse Numérique, Université P. et M. Curie, 4 Place Jussieu, 75230 Paris Cedex, France
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Synopsis

In this paper, we prove various existence and non-existence results for semilinear elliptic problems in unbounded domains. In particular we prove for general classes of unbounded domains that there exists no solution distinct from 0 of

for any smooth f satisfying f(0) = 0. This result is obtained by the use of new identities that solutions of semilinear elliptic equations satisfy.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 1-2 , 1982 , pp. 1 - 14
Copyright
Copyright © Royal Society of Edinburgh 1982

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