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Nonlinear periodic parabolic problems with nonmonotone discontinuities

Published online by Cambridge University Press:  20 January 2009

Dimitrios A. Kandilakis  and
Nikolaos S. Papageorgiou
Dimitrios A. Kandilakis
Affiliation:
Department of Mathematics, University of the Aegean, 83200 Karlovassi Samos, Greece
Nikolaos S. Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus 15780 Athens, Greece
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Abstract

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In this paper we consider a nonlinear periodic parabolic boundary value problem with a discontinuous nonmonotone nonlinearity. Using a lifting result for operators of type (S+), a general surjectivity theorem for operators of monotone type and an auxiliary problem defined by truncation and penalization we prove the existence of a solution in the order interval formed by an upper and lower solution. Moreover we show that the set of all such solutions is compact in Lp(T, (Z)).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 1 , February 1998 , pp. 117 - 132
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

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