Existence of periodic solutions to a pp-Laplacian Liénard differential equation with a deviating argument

By means of Mawhin’s continuation theorem, a kind of pp-Laplacian Liénard differential equation with a deviating argument as follows: (ϕp(y′(t)))′=f(y(t))y′(t)+h(y(t))+g(y(t−τ(t)))+e(t)(ϕp(y′(t)))′=f(y(t))y′(t)+h(y(t))+g(y(t−τ(t)))+e(t) is studied. A new result on the existence of periodic solutions is obtained. The interest is that the relation between the existence of periodic solutions and the deviating argument τ(t)τ(t) is investigated. Meanwhile, the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature.