| Impulsive differential equations serve as basic models to study the dynamics ofprocesses that are subject to sudden changes in their states. This thesis deals withthe existence and multiplicity of periodic solutions (harmonics and subharmonics) ofthe superlinear Duffing equation with impulsive effects. The phase-plane method isusea to investigate the properies of impulsive diffential equations. We consider thePoincarémap of impulsive differential equation as a composition of some flows andsome jump mappings caused by impulse. Then, under some reasonable assumption, wehave proved the Poincarémap is a twist area-preserving homeomorphism. Therefore, wecan obtain the existence and multiplicity of fixed point for Poincarémap which impliesthe existence and multiplicity of periodic solutions (harmonics and subharmonics) ofthe superlinear Duffing equation with impulsive effects.
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