Abstract :
In this paper, we study the existence problem of anti-periodic solutions for the following
first-order nonlinear evolution equation:
u
(t )+ Au(t )+ F(t,u(t)) = 0, t∈ R,
u(t + T )=−u(t ), t ∈ R,
in a Hilbert space H, where A is a self-adjoint operator and F is a continuous nonlinear
operator. An existence result is obtained under assumptions that D(A) is compactly
embedded into H and F is anti-periodic and bounded by a L2 function. Furthermore,
anti-periodic solutions for second-order equations are also studied.
2002 Elsevier Science (USA). All rights reserved.
