Periodic trajectories for evolution equations in Banach spaces

Abstract

The existence of periodic solutions for the evolution equation y'(t) + Ay(t) ∋ F(t, y(t)) is investigated under considerably simple assumptions on A and F. Here X is a Banach space, the operator A is m-accretive, -A generates a compact semigroup, adn F is a Carathéodory mapping. Two examples concerning nonlinear parabolic equations are presented.