Asymptotic Properties of Neutral Differential Equations with Variable Coefficients

Abstract

The aim of this work is to study oscillatory behavior of solutions for even-order neutral nonlinear differential equations. By using the Riccati substitution, a new oscillation conditions is obtained which insures that all solutions to the studied equation are oscillatory. The obtained results complement the well-known oscillation results present in the literature. Some example are illustrated to show the applicability of the obtained results.

Neutral Differential Equations of Higher-Order in Canonical Form: Oscillation Criteria

“…It is easy to see that Equation (60) in Example 1 oscillates at any value of φ 0 > 0. Furthermore, through this paper, we were able to extend previous results in the literature, which can be applied more widely compared to [14,15,19].…”

“…Several researchers have investigated the oscillatory behaviour of even-order DEs under various conditions. For more information, see [12][13][14][15][16][17][18][19][20]. We mention in some detail:…”

“…+ φ(t)x (δ(t)) = 0 some oscillation criteria were established by Bazighifan et al [14], where 0 ≤ g(t) < g 0 < ∞ and (3) hold.…”