Existence of periodic solutions for a pp-Laplacian neutral functional differential equation

In this paper, the author study the existence of periodic solutions for a pp-Laplacian neutral functional differential equation as follows [φp((u(t)−∑j=1ncju(t−rj))′)]′=f(u(t))u′(t)+α(t)g(u(t))+∑j=1nβj(t)g(u(t−γj(t)))+p(t). By analyzing some properties of operator A:CT→CT,(Ax)(t)=x(t)−∑i=1ncix(t−ri), and then using continuation theorem of coincidence degree theory developed by Mawhin, some new results on the existence of periodic solutions are obtained. The example shows that the results of this paper are more general and easily applicable, and improve and generalize some corresponding ones of the known literature.