Amended oscillation criteria for second-order neutral differential equations with damping term

Abstract

The aim of this work is to improve the oscillation results for second-order neutral differential equations with damping term. We consider the noncanonical case which always leads to two independent conditions for oscillation. We are working to improve related results by simplifying the conditions, based on taking a different approach that leads to one condition. Moreover, we obtain different forms of conditions to expand the application area. An example is also given to demonstrate the applicability and strength of the obtained conditions over known ones.

New Oscillation Theorems for Second-Order Superlinear Neutral Differential Equations with Variable Damping Terms

“…Remark 1. All results presented in references [15,16,[18][19][20][21][22][23][24] are not applicable to example (22); this is because the function is oscillatory, whereas all the results in the references are applied by assuming d( ) is a positive function.…”

“…Damped DEs find numerous important applications in various fields of science and engineering. This type of equation is involved in the study of dynamical systems that exhibit oscillatory behavior and are influenced by damping effects [4,15]. For instance, in the field of civil engineering, these equations help understand the vibrations of buildings, bridges, and other structures subjected to external forces or disturbances.…”

“…Moreover, the authors in [15,16,[18][19][20][21][22][23] studied Equation ( 1) and special forms thereof and concluded that some oscillatory results occur in the presence of the condition γ ∈ [0, 1). Several significant results have been presented regarding the oscillatory behavior of secondorder neutral differential equation solutions with a damping term.…”

Oscillation results for a certain class of fourth-order nonlinear delay differential equations

“…In the past decade, there has been increasing interest in obtaining oscillation and nonoscillation criteria of different classes of third and fourth-order differential equations. The works [2, 3,4,5,6,7,8,9,10,11,12,13] improved the oscillation criteria for second-order equations with delay and advanced argument. For even-order delay equations, papers [15,16,17,18,19,20,21,22,23,24,25,26,27] developed the oscillation criteria.…”

New oscillation theorems for a class of even-order neutral delay differential equations

“…Very recently, a great development was found in the study of the oscillatory properties of solutions of second order neutral-delay differential equations; see for examples [5][6][7][8][9][10][11][12][13][14][15][16][17]. It would be interesting to extend this development to higher-order differential equations.…”