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

Norimichi Hirano and Naoki Shioji

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

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.