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Existence and multiplicity result for a class of second order elliptic equations

Published online by Cambridge University Press:  14 November 2011

Helmut Hofer
Helmut Hofer
Affiliation:
Mathematics Institute, University of Zurich, Freiestrasse 36, CH-8032 Zurich, Switzerland
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Synopsis

Some second order semilinear elliptic boundary value problems of the Ambrosetti-Prodi-type are studied. Existence and multiplicity of solutions is proved in dependence on a parameter. Constructing a global strongly increasing fixed point operator in a suitable function space, observing - under appropriate conditions, which are in some sense optimal–that the fixed point operator has some properties similar to a strongly positive linear endomorphism, one unifies and improves the treatment of such problems, whether the nonlinearity is dependent on the gradient or not, and obtains some new results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 1-2 , 1981 , pp. 83 - 92
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

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