Existence of periodic solutions for first-order evolution equations without coercivity

In this paper, we study the existence problem of periodic solutions for the following first-order nonlinear evolution equation u (t )+A(t)u(t)+F t,u(t) 0, t∈ R, u(t + T ) = u(t ), t ∈ R, in a Hilbert space H, where A is a monotone type operator and F is a nonlinear operator. Existence results are obtained without assuming the coercivity condition.  2003 Elsevier Inc. All rights reserved