Existence of periodic solutions for a pp-Laplacian neutral functional differential equation with multiple variable parameters

By means of Mawhin’s continuation theorem, a kind of p-Laplacian neutral functional differential equation with multiple variable parameters as follows: (φp((u(t)−∑i=1nci(t)u(t−ri))′))′=f(u(t))u′(t)+α(t)g(u(t))+∑j=1nβj(t)g(u(t−γj(t)))+e(t), is studied. The interesting thing is that the coefficient cc is not a constant, by analyzing some properties of operator A:CT→CT,[Ax](t)=x(t)−∑i=1nci(t)x(t−ri) and then using Mawhin’s continuation theorem, some new results on the existence of periodic solutions are obtained.