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On the maximum of solutions for a semilinear elliptic problem

Published online by Cambridge University Press:  14 November 2011

Guido Sweers
Guido Sweers
Affiliation:
Faculty of Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ Delft, The Netherlands
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Synopsis

In this paper we study some properties of a semilinear elliptic eigenvalue problem with nondefinite right-hand side. In the first part we show that every solution will have its maximum in some specified interval J. If the domain is inside a cone in ℝN with N > 1, then J is strictly smaller than in the one-dimensional case. In the second part we show, for bounded domains, that if the maximum is inside some subinterval of J, then for any eigenvalue there will be at most one solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 108 , Issue 3-4 , 1988 , pp. 357 - 370
Copyright
Copyright © Royal Society of Edinburgh 1988

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