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Nontrivial full bounded solutions of time-periodic semilinear parabolic PDEs

Published online by Cambridge University Press:  14 November 2011

Marian Mrozek  and
Krzysztof P. Rybakowski
Marian Mrozek
Affiliation:
Uniwersytet Jagielloński, Katedra Informatyki, ul. Kopernika 27, 31-501 Kraków, Poland
Krzysztof P. Rybakowski
Affiliation:
Albert-Ludwigs-Universität, Institut für Angewandte Mathematik, Hermann-Herder Straße 10, 7800 Freiburg, West Germany
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Synopsis

Consider the semilinear evolution equation

(P) u + Au = f(t,u)

where A is a sectorial operator on a Banach space and f is ω-periodic in t. Using a time-discrete Conley index developed in a previous paper [6], we prove a few existence results on bounded solutions of (P) defined for all t ∊ R. More specific results are given for time-periodic scalar parabolic equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 3-4 , 1991 , pp. 305 - 315
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

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