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

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.