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Extremal solutions and strong relaxation for nonlinear periodic evolution inclusions

Published online by Cambridge University Press:  20 January 2009

Nikolaos S. Papageorgiou  and
Nikolaos Yannakakis
Nikolaos S. Papageorgiou
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece (npapg@math.ntua.gr)
Nikolaos Yannakakis
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece (npapg@math.ntua.gr)
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Abstract

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We study the existence of extremal periodic solutions for nonlinear evolution inclusions defined on an evolution triple of spaces and with the nonlinear operator establish A being time-dependent and pseudomonotone. Using techniques of multivalued analysis and a surjectivity result for L-generalized pseudomonotone operators, we prove the existence of extremal periodic solutions. Subsequently, by assuming that A(t, ·) is monotone, we prove a strong relaxation theorem for the periodic problem. Two examples of nonlinear distributed parameter systems illustrate the applicability of our results.

Keywords

periodic solutionevolution triplecompact embeddingmonotone operatorpseudomonotone operatorL-generalized pseudomonotone operator
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 569 - 586
Copyright
Copyright © Edinburgh Mathematical Society 2000

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