ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR A p-LAPLACIAN NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH TIME-VARYING OPERATOR

In this paper, a kind of p-Laplacian neutral functional differential equation with time- varying operator as follows � ϕpu � (t) − n ∑ i=1 ci(t)u � (t −ri) � � � = f(u � (t))+β(t)g(u(t −γ(t)))+e(t), is studied and some new results are obtained. It is worth noting that the parameters ci(t)(i = 1,2,···,n) are functions and the coefficient β(t) (which is ahead of g) is sign-variable here. It is interesting, but it is so challenging and difficult that few people have discussed it so far.