NEW RESULTS ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR A HIGHER-ORDER P-LAPLACIAN NEUTRAL DIFFERENTIAL EQUATION WITH MULTIPLE DEVIATING ARGUMENTS

In this article, we consider the following high-order p-Laplacian neutral differential equation with multiple deviating arguments: (phi(p)(x(t) - cx(t - r))((n))(t)))((m)) = f(x(t))x'(t) + g(t, x(t), x(t - tau(1)(t)), ..., x(t - tau(k)(t))) + e(t). By applying the continuation theorem and some analytic techniques, sufficient conditions for the existence of periodic solutions are established. It is interesting that the equations not only depend on the constant c but are also dependent on the deviating arguments tau(i), i = (1,..., k).