Infinitely many periodic solutions of Duffing equations under integral condition

Nannan Zheng, Zaihong Wang

DOI: http://dx.doi.org/10.12775/TMNA.2020.017

Abstract


In this paper, we study the multiplicity of periodic solutions of a Duffing equation $$ x''+g(x)=p(t). $$% By using the generalized Poincaré-Birkhoff fixed point theroem, we prove that this equation has infinitely many periodic solutions provided $g$ satisfies a kind of integral condition and the related time map satisfies oscillating condition.

Keywords


Duffing equation; periodic solution; Poincaré-Birkhoff fixed point theorem

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References


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