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The number of positive solutions of a non-linear problem with discontinuous non-linearity

Published online by Cambridge University Press:  14 November 2011

Jacques Douchet
Jacques Douchet
Affiliation:
Ecole Polytechnique Fédérale de Lausanne, 61 avenue de Cour, 1007 Lausanne, Switzerland
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Synopsis

For the non-linear problem

where f is a discontinuous function at 1, we show that the number of non-trivial positive solutions, for a given real number λ≧0, is related to the graph of a continuous function g. Then, by studying the function g it is possible in some special cases to give, for any λ≧0, the minimal or exact number of non-trivial positive solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 3-4 , 1981 , pp. 281 - 291
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

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