Abstract and Applied Analysis
Volume 2004 (2004), Issue 3, Pages 183-203
doi: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 Norimichi Hirano and Naoki Shioji. 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 K≠D(A)¯, we study Cauchy problems
and periodic problems for nonlinear evolution equation u(t)∈K, u′(t)+Au(t)∋f(t,u(t)), 0≤t≤T, 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]×(K∩V)→H is of Carathéodory
type.