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Periodic Solutions of a Class of Duffing DifferentialEquations
  
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KeyWord:Periodic solution  averaging method  Duffing differential equa- tion  bifurcation  stability
Author NameAffiliation
Rebiha Benterki Departement de Mathematiques, Universite de Bordj Bou Arreridj, Bordj Bou Arreridj 34265, Elanasser, Algeria 
Jaume Llibre Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain 
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Abstract:
      In this work we study the existence of new periodic solutions for the well knwon class of Duffing differential equation of the form $x^{\prime\prime}+ c x^{\prime}+ a(t) x +b(t) x^3 = h(t)$, where $c$ is a real parameter, $a(t)$, $b(t)$ and $h(t)$ are continuous $T$--periodic functions. Our results are proved using three different results on the averaging theory of first order.