On the Qualitative Behavior of Third-Order Differential Equations with a Neutral Term

Abstract

In this paper, we analyze the asymptotic behavior of solutions to a class of third-order neutral differential equations. Using different methods, we obtain some new results concerning the oscillation of this type of equation. Our new results complement related contributions to the subject. The symmetry plays a important and fundamental role in the study of oscillation of solutions to these equations. An example is presented in order to clarify the main results.

Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations

“…A. Soliman et al [20]. Recently, for β 1 = n = 1 and 0 ≤ p(ς) ≤ p 0 ≤ ∞, Equation (1), its particular cases and modifications have been studied by Y. Jiang et al [11], T. Li et al [4], R. Elayaraja et al [12].…”

On the Oscillation of Solutions of Differential Equations with Neutral Term

“…Xing et al [9] and Moaaz et al [10] also extended this evolution to differential equations of the neutral type. Therefore, there are many studies on the oscillatory and asymptotic behavior of different orders of some differential equations, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order

“…Because of the enormous advantage of neutral differential equations in describing several neutral phenomena, there is great scientific and academic value in studying neutral differential equations, both theoretically and practically; see [1]. Lately, there have been numerous articles investigating the oscillation of the solutions of third/higher order neutral differential equations with/without deviating arguments; see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”