Periodic solutions for a higher-order p-Laplacian neutral differential equation with multiple deviating arguments

Abstract

In this article, we consider the following high-order p-Laplacian neutral differential equation with multiple deviating arguments: $$(\varphi_{p}(x(t)-cx(t-r))^{(m)}(t)))^{(m)}= f(x(t))x'(t)+g(t,x(t),x(t-\tau_{1}(t)),...,x(t-\tau_{k}(t)))+e(t).$$ By appling the continuation theorem, theory of Fourier series, Bernoulli numbers theory and some analytic techniques, sufficient conditions for the existence of periodic solutions are established.