TY - JOUR
T1 - Periodic Solutions of a Class of Duffing Differential Equations
AU - Benterki , Rebiha
AU - Llibre , Jaume
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 167
EP - 177
PY - 2021
DA - 2021/04
SN - 1
DO - http://doi.org/10.12150/jnma.2019.167
UR - https://global-sci.org/intro/article_detail/jnma/18855.html
KW - Periodic solution, averaging method, Duffing differential equation, bifurcation, stability.
AB - <p style="text-align: justify;">In this work we study the existence of new periodic solutions for the well known 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.</p>