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A multiplicity result for a class of elliptic boundary value problems

Published online by Cambridge University Press:  14 November 2011

Herbert Amann  and
Peter Hess
Herbert Amann
Affiliation:
Mathematisches Institut, Universität Zürich, Freiestrasse 36, CH-8032 Zürich, Switzerland
Peter Hess
Affiliation:
Mathematisches Institut, Universität Zürich, Freiestrasse 36, CH-8032 Zürich, Switzerland
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Synopsis

We consider a mildly nonlinear elliptic boundary value problem depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we derive lower bounds on the number of solutions. The results complement an earlier theorem due to Kazdan and Warner [6].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 145 - 151
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

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Note added in proof, 31 July 1979. After this paper had been submitted for publication the authors became aware of an article by Dancer, E. N., On the ranges of certain weakly nonlinear elliptic partial differentialequations, J. Math. Pure Appl. 57 (1978), 351–366. In that paper a similar result is proved by closely related considerations.Google Scholar