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Abstract and Applied Analysis
Volume 2004, Issue 3, Pages 183-203
http://dx.doi.org/10.1155/S1085337504311073

Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems

Department of Mathematics, Graduate School of Environment and Information Sciences, Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan

Received 11 August 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the case of KD(A)¯, we study Cauchy problems and periodic problems for nonlinear evolution equation u(t)K, u(t)+Au(t)f(t,u(t)), 0tT, where A isa maximal monotone operator on a Hilbert space H, K is a closed, convex subset of H, V is a subspace of H, and f:[0,T]×(KV)H is of Carathéodory type.