EXISTENCE, UNIQUENESS AND STABILITY OF PERIODIC SOLUTIONS OF A DUFFING EQUATION UNDER PERIODIC AND ANTI-PERIODIC EIGENVALUES CONDITIONS

Abstract

Using periodic and anti-periodic eigenvalues, we present new criteria for guaranteeing the existence, uniqueness and asymptotic stability (in the sense of Lyapunov) of periodic solutions of a Duffing equation under conditions which are weaker than those used in the literature. The proof is based on the application of the existence theorem of Leray-Schauder type, Floquet theory, Lyapunov stability theory and some analytic techniques.