Abstract
The paper is devoted to the study of oscillation of even-order neutral differential equations. New Kamenev-type oscillation criteria are established, and they essentially improve and complement some the well-known results reported in the literature. Ideas of symmetry help us determine the correct ways to study these topics and show us the correct direction, because they are often invisible. To illustrate the main results, some examples are mentioned.
Highlights
The objective of this paper is to investigate the oscillation of solutions to the following equation: a ( υ ) u ( n −1) ( υ )
Zhang et al [25] examined the oscillation of even-order neutral differential equations u(n) (υ) + q (υ) f (y (δ (υ))) = 0
From ([19], Corollary 1), we have that the associated differential Equation (7) has a positive solution, which yields a contradiction
Summary
The objective of this paper is to investigate the oscillation of solutions to the following equation:. Zhang et al [25] examined the oscillation of even-order neutral differential equations u(n) (υ) + q (υ) f (y (δ (υ))) = 0. Symmetry 2020, 12, 555 and established the criteria for the solution to be oscillatory when 0 ≤ p (υ) < 1. In this article, using the technique of Riccati and comparison with first-order differential equations, we establish new Kamenev-type oscillation criteria of an even-order neutral differential equation.
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