Antiperiodic solutions for semilinear evolution equations
In this paper, we study the existence problem of antiperiodic solutions for the following first-order semilinear evolution equation: u'(t) + Au(t) + partial derivativeGu(t) + f(t) = 0, t is an element of R; u(t + T) = -u(t), t is an element of R, in a Hilbert space H, where A is a self-adjoint operator, partial derivativeG is the gradient of G. Existence results are obtained under assumptions that D(A) is compactly embedded into H and partial derivativeG is continuous or G is a convex function, which extend some known results in [1,2]. (C) 2004 Elsevier Ltd. All rights reserved.
antiperiodic solution semilinear evolution equation self-adjoint operator