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This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: xÃ¢Â€Â²Ã¢Â€Â²(t)+ÃŽÂ±xÃ¢Â€Â²(t)+ÃŽÂ²x(t)=f(t,x(t),x(ÃŽÂ±1(t)),Ã¢Â€Â¦,x(ÃŽÂ±n(t))),Ã¢Â€Â‰a.e.Ã¢Â€Â‰Ã¢Â€Â‰tÃ¢ÂˆÂˆ[0,T],Ã¢Â€Â‰ÃŽÂ”x(tk)=Ik(x(tk),xÃ¢Â€Â²(tk)),Ã¢Â€Â‰k=1,   Ã¢Â€Â¦,m,Ã¢Â€Â‰ÃŽÂ”xÃ¢Â€Â²(tk)=Jk(x(tk),xÃ¢Â€Â²(tk)),Ã¢Â€Â‰k=1,Ã¢Â€Â¦,m,Ã¢Â€Â‰x(i)(0)=x(i)(T),Ã¢Â€Â‰i=0,1. Sufficient conditions are established for the existence of at least one solution of above-mentioned boundary value problem. Our method is based upon Schaeffer's fixed-point theorem. Examples are presented to illustrate the efficiency of the obtained results

Existence of Solutions of Periodic Boundary Value Problems for Impulsive Functional Duffing Equations at Nonresonance Case