Existence of periodic solutions for second-order neutral differential equations

By means of variational structure and critical point theory, we study the existence of periodic solutions for a second-order neutral differential equation $$displaylines{ (p(t) x' (t - au ))' + f(t, x(t), x(t-au ), x(t-2au) ) = g(t),cr x(0) = x(2kau), x'(0) = x'(2kau). }$$ where $k$ is a given positive integer and $au$ is a positive number.