New results on the existence of periodic solutions to a p-Laplacian differential equation with a deviating argument

By means of Mawhin's continuation theorem, a kind of p-Laplacian differential equation with a deviating argument as follows:(φp(x′(t)))′=f(t,x(t),x(t−τ(t)),x′(t))+e(t)(φp(x′(t)))′=f(t,x(t),x(t−τ(t)),x′(t))+e(t) is studied. Some new results on the existence of periodic solutions are obtained. The main results (Theorems 3.2 and 3.3) are all related to the deviating argument τ(t)τ(t). Meanwhile, the degrees with respect to the variables x0,x1x0,x1 of f(t,x0,x1,x2)f(t,x0,x1,x2) are allowed to be grater than p−1p−1, which is different from the corresponding conditions of known literature.