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≤α<1 there exists a constant K_α, depending only on α, such that if f:D(A^α)→X satisfies{norm of matrix}f(u)-f(v){norm of matrix} X≤L{norm of matrix} Aα(u-v){norm of matrix} X then any periodic orbit of the equation u̇=-Au+f(u) has period at least K_αL^-1/(1-α). This generalises our previous result [J.C. Robinson, A. Vidal-López, Minimal periods of semilinear evolution equations with Lipschitz nonlinearity, J. Differential Equations 220 (2006) 396-406] which was restricted to 0≤α≤1/2 and A^-1 compact.