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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 4, 1998, pp. 859–875
DOI: 10.4171/ZAA/855

Published online: 1998-12-31

Solutions and Periodic Solutions for Nonlinear Evolution Equations with Non-Monotone Perturbations

E.P. Avgerinos[1] and Nikolaos S. Papageorgiou[2]

(1) University of the Aegean, Rhodos, Greece
(2) National Technical University of Athens, Greece

In this paper we solve periodic and Cauchy problems for nonlinear evolution equa-tions driven by time-dependent, pseudomonotone operators and a non-monotone perturbation term. Our proof produces as a by-product a useful property of the solution map for maximal monotone problems. Two examples of nonlinear parabolic problems illustrate the applicability of our work.

Keywords: Evolution triples, compact embeddings, coercive operators, pseudomonotone operators, L-pseudomonotone operators, surjectivity results, demicontinuity, parabolic problems

Avgerinos E.P., Papageorgiou Nikolaos: Solutions and Periodic Solutions for Nonlinear Evolution Equations with Non-Monotone Perturbations. Z. Anal. Anwend. 17 (1998), 859-875. doi: 10.4171/ZAA/855