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

Abstract

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.