Email: info@jnma.ca

ISSN 2562-2854 (print)

ISSN 2562-2862 (online)

# Periodic solutions of the Duffing differential equation revisited via the averaging theory

Rebiha Benterki and Jaume Llibre

We use three different results of the averaging theory of first order for studying the existence of new periodic solutions in the two Duffing differential equations $\ddot y+ a \sin y= b \sin t$ and $\ddot y+a y-c y^3=b\sin t$, where $a$, $b$ and $c$ are real parameters.