Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations

Abstract

Existence and Lyapunov stability of periodic solutions for a generalized higher-order neutral differential equation are established.

On high-order generalized neutral singular differential equations with time-dependent deviating argument

“…In 2009, Ren and Cheng [13] discussed the following high-order neutral differential equation (φ p (x(t) − cx(t − τ)) (l) ) (n−l) = F(t, x(t), x (t), • • • , x (l−1) (t)), (1.1) where p ≥ 2, φ p (x) = |x| p−2 x for x = 0 and φ p (0) = 0. The existence of periodic solutions for equation (1.1) was obtained in the general case (i.e., |c| = 1 in [12]) and in the critical case (i.e. |c| = 1 in [13]), respectively.…”

“…In this paper, inspired by the results presented in [4,12,13,14,15], we discuss the existence of a positive periodic solution for the following high-order p-Laplacian generalized neutral singular differential equation with time-dependent deviating argument…”