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Monotone techniques and semilinear elliptic boundary value problems*

Published online by Cambridge University Press:  14 November 2011

K. J. Brown  and
S. S. Lin
K. J. Brown
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh
S. S. Lin
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh
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Synopsis

This paper considers semilinear elliptic boundary value problems of the form

where the partial derivative ∂f/∂u is bounded above by the least eigenvalue of the linear elliptic operator L. Existence and uniqueness of solutions is proved by using monotone operator theory and sub and supersolution techniques.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 1-2 , 1978 , pp. 139 - 149
Copyright
Copyright © Royal Society of Edinburgh 1978

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