Semilinear Duffing Equations Crossing Resonance Points

In this paper, using a generalized form of the Poincaré–Birkhoff theorem and a fixed point theorem, we prove, under weaker conditions, two theorems for the equationx+g(x)=p(t),p(t)≡p(t+2π), of which one shows the existence of a harmonic solution, the other that the equation may have an infinite number of harmonic solutions in the resonance case. This is an enhancement of the results already obtained.