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BOUNDARY VALUE PROBLEMS VIA AN INTERMEDIATE VALUE THEOREM

Published online by Cambridge University Press:  01 September 2008

GERD HERZOG  and
ROLAND LEMMERT
GERD HERZOG
Affiliation:
Institut für Analysis, Universität Karlsruhe, D-76128 Karlsruhe, Germany e-mails: Gerd.Herzog@math.uni-karlsruhe.de; Roland.Lemmert@math.uni-karlsruhe.de
ROLAND LEMMERT
Affiliation:
Institut für Analysis, Universität Karlsruhe, D-76128 Karlsruhe, Germany e-mails: Gerd.Herzog@math.uni-karlsruhe.de; Roland.Lemmert@math.uni-karlsruhe.de
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Abstract

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We use an intermediate value theorem for quasi-monotone increasing functions to prove the existence of the smallest and the greatest solution of the Dirichlet problem u″ + f(t, u) = 0, u(0) = α, u(1) = β between lower and upper solutions, where f:[0,1] × E → E is quasi-monotone increasing in its second variable with respect to a regular cone.

Keywords

34B1534C1234G20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 531 - 537
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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