Oscillation criteria for second-order nonlinear delay dynamic equations of neutral type

Abstract

We investigate oscillatory behavior of solutions to a class of second-order nonlinear neutral delay dynamic equations with nonpositive neutral coefficients. In particular, we study the corresponding noncanonical neutral differential equations. New oscillation criteria are established that complement and improve related contributions to the subject. An example is given to illustrate the main results. MSC: 34K11; 34N05

New Oscillation Criteria for Second Order Half-Linear Neutral Type Dynamic Equations on Time Scales

“…holds. For more details, see [13] [14] [15] [16]. When =  , we refer the reader to [17] [18] [19] [20] and the references cited therein.…”

“…b a r t x t x t p t x t x t p t x t q s f x g s In recent years, there has been an increasing interest in the study of the oscillatory behavior of solutions of dynamic equations. We refer to the papers [1]- [16] and the references cited therein.…”

Oscillation theorems for fourth-order hybrid nonlinear Functional dynamic equations with damping

“…Equation ( 1) is called oscillatory if all its solutions are oscillatory. Recently, there has been an increasing interest in obtaining sufficient conditions for oscillation and nonoscillation of solutions of various dynamic equations, we refer the reader to the articles [3,4,6,10,11,13,21,22,28,36,40] and the references cited therein. In recent years, there has been much research activity concerning the hybrid differential equation, the reason is that hybrid differential equations generalize ideas from dynamic systems.…”

Oscillation of nonlinear neutral dynamic equations on time scales

“…By employing a Riccati transformation technique and applying some inequalities, a large number of papers have been devoted to the oscillatory behavior of solutions to second order dynamic equations with nonnegative neutral coefficients; for example, see [3,8,9,[23][24][25][26][27] and the references cited therein. At the same time, there are comparatively few papers concerned with the oscillation of equations with nonpositive neutral coefficients; for example, see [7,14,18,20,28].…”

“…Recently, Zhang et al [28] discussed the neutral dynamic equation where z(ℓ) = x(ℓ) − p(ℓ)x(τ (ℓ)) , α ≥ 1 is a quotient of odd positive integers, 0 ≤ p(ℓ) ≤ p 0 < 1 , and there is a positive constant k such that f (x)…”