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).(φp(x′(t)))′=Cx′(t)+g(t,x(t),x(t−τ(t)))+e(t). 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,vu,v imposed on g(t,u,v)g(t,u,v) is allowed to be greater than p−1p−1, so our results generalize and improve on the corresponding results in related papers.