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l-generalized pseudomonotone operator

Proceedings of the Edinburgh Mathematical Society (1)

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Extremal solutions and strong relaxation for nonlinear periodic evolution inclusions
Nikolaos S. Papageorgiou, Nikolaos Yannakakis
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Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 3 / October 2000

Published online by Cambridge University Press:

20 January 2009, pp. 569-586
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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.