Existence and uniqueness of periodic solution for a class of semilinear evolution equations

摘要

This paper deals with the existence and uniqueness for the periodic boundary value problem of the semilinear evolution equation in a Hilbert space H { u '(t) + Au(t) = f(t, u (t1)), 0 < t < omega, u (0) = u(omega) where A : D(A) subset of H -> H is. a positive definite self-adjoint operator, omega > 0 and f: [0,omega] x H -> H satisfy Caratheodory condition. We present some spectral conditions for the nonlinearity f(t. u) to guarantee the existence and uniqueness. These spectral conditions are the generalization for nonresonance condition of the self-adjoint elliptic boundary value problems. (C) 2008 Published by Elsevier Inc