Existence of Periodic Solution for a Kind of ($m$, $n$)-Order Generalized Neutral Differential Equation

Abstract

In this paper, we consider the following high-order $p$-Laplacian generalized neutral differential equation with variable parameter
$(φ_p(x(t)− c(t)x(t− σ))^{(n)})^{(m)} + g(t, x(t), x(t− τ (t)), x′(t), · · · , x^{(m)}(t)) = e(t)$.
By the coincidence degree theory and some analysis skills, sufficient conditions for the existence of periodic solutions are established.