Periodic solutions to a second order pp-Laplacian neutral functional differential system

By analyzing some properties of the linear difference operator A:[Ax](t)=x(t)−Cx(t−τ)A:[Ax](t)=x(t)−Cx(t−τ) first, and then using an extension of Mawhin’s continuation theorem, a second order pp-Laplacian neutral functional differential system as follows ddtϕp[(x(t)−Cx(t−τ))′]=f(t,x(t),x(t−μ(t)),x′(t)) is studied. Some new results on the existence of periodic solutions is obtained. The result is related to the deviating arguments ττ and μμ. Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature.