Abstract
The purpose of this paper is to give new criteria for the exact multiplicity and stability of 2π-periodic solutions for Duffing equation x′′ + cx′ + g(t, x) = h(t). The proof is based on the connections between degree theory and local index of periodic solutions due to Ortega [17], and the new Lp estimates (1 ≤ p ≤ ∞) for periodic and anti-periodic eigenvalues of Hill’s equation due to Zhang and Li [26]. The class of g(t, x) has been greatly generalized.
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