The existence of anti-periodic solutions for high order Duffing equation (Q949318)

The authors prove the existence of anti-periodic solutions for a \(n\)-th order differential equation of the type \[ x^{(n)}+\sum_{i=1}^{n-1}a_i x^{(i)}+g(t,x)=p(t). \] The assumptions imply nonresonance, since the nonlinearity in some sense asymptotically lies below the first eigenvalue of the differential operator. The proof is carried out by the use of Leray-Schauder degree theory.