Consider the Duffing's equation x+g(x)=p(t) where g ∈ C1(R) and p(t)∈ C(R) is a 2π- periodic, with g(x) statisfying condition g′ (x) < 0 , the necessary and sufficient conditions to ensure the existence and uniqueness of 2π- periodic solution of Duffing equation are obtained by means of coincidence degree.
