Minimal periods of semilinear evolution equations with Lipschitz nonlinearity revisited

We show that when A is a self-adjoint sectorial operator on a Hilbert space, for 0 <= alpha <= 1 there exists a constant K alpha, depending only on a, such that if f :D(A(alpha)))- X satisfies parallel to f (u) - f (v)parallel to(x) <= L parallel to A(alpha) (u - v)parallel to(x) then any periodic orbit of the equation u = -Au f(u) has period at least K alpha L-1/(1-alpha). This generalises our previous result [J.C. Robinson, A. Vidal-Lopez, Minimal periods of semilinear evolution equations with Lipschitz nonlinearity, J. Differential Equations 220 (2006) 396-406] which was restricted to 0 <= alpha <= 1/2 and A(-1) compact