Existence and uniqueness of periodic solutions for a p-Laplacian Duffing equation with a deviating argument

By means of Mawhin’s continuation theorem, we study a class of p-Laplacian Duffing type differential equations of the form

(_φp(x^′(t)))^′=Cx^′(t)+g(t,x(t),x(t−τ(t)))+e(t).${\left({\phi }_p\left(x^{\prime }\left(t\right)\right)\right)}^{\prime }=C{x}^{\prime }\left(t\right)+g(t,x\left(t\right),x(t-\tau \left(t\right)))+e\left(t\right)\text{.}$

Some new results on the existence and uniqueness of periodic solutions for the above equation are obtained. It is significant that the growth degree with respect to the variables u,v$u,v$ imposed on g(t,u,v)$g(t,u,v)$ is allowed to be greater than p−1$p-1$, so our results generalize and improve on the corresponding results in related papers.