Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces (Q2804258)

The authors prove the existence of periodic solutions to evolution equations and study their conditional stability. There are three methods to prove the existence of periodic solutions to semilinear evolution equations. One is the fixed point method, one is concerned with the Poincaré map. The other is an ergodic approach, that is, the method of Cesaro limit and relevant admissible function spaces, which is applied in the present paper. The results in this paper generalize the evolution equation with uniformly Lipschitz perturbation to the locally Lipschitz case.