# Oscillation theorems for second-order nonlinear neutral delay dynamic equations on time scales

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In this work, we use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation (p(t)(xÎ” (t)) Î³)Î” +q(t)f(x(Ï„(t)))=0, on a time scale T, where Î³ is the quotient of odd...

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By employing a generalized Riccati transformation and the averaging technique, some new oscillation criteria for second-order nonlinear differential equation of the form ï¼ˆr(t)Î¨(x(t))|x'(t)Î±-1x'(t)ï¼‰' + f(t,x(t),x'(t)) = 0, t â‰¥ t0 are established. Several examples are also...

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A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the PadÃ© approximants. The proposed method introduces an alternative framework...

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This paper is concerned with a class of even order nonlinear differential equations of the form d/dt(|(x(t) + p(t)x(t(t)))(n-1)|a-1(x(t) + p(t)x(tt(t)))(n-1) + F(t,x(g(t))) = 0, where n is even and t = t0. By using the generalized Riccati transformation and the averaging technique, new...

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The article examines closed quasilinear control systems which applies a scalar periodic nonlinearity. It presents theorems on the existence of sequences of periodic oscillations with unbounded amplitudes, and analyzes perturbations of the original autonomous system under certain conditions....

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Some new criteria for the oscillation of fourth-order nonlinear functional differential equations of the form are established.

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We study the solutions to high-order linear functional differential equations with impulses. We improve previous results in the oscillation theory for ordinary differential equations and obtain new criteria on the oscillation of solutions.

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We establish conditions for the linear differential equation y(n)(t) + p(t)y(g(t)) = 0 to have property A. Explicit sufficient conditions for the oscillation of the the equation is obtained while dealing with the property A of the equations. A comparison theorem is obtained for the oscillation...

- Oscillation and Nonoscillation Theorems for a Class of Fourth Order Quasilinear Difference Equations. LIU LanChu; GAO Youwu // Studies in Mathematical Sciences;2/28/2013, Vol. 6 Issue 1, p26
In this paper, we consider certain quasilinear difference equations (A) Î”Â²(|Î”Â²Yn | Î±-1 Î”Â²Yn)+ qn|YÏ„(n) |Î²-1 YÏ„(n) = 0 where (a) Î±,Î² are positive constants; (b) {qn}n0âˆž are positive real sequences. n0 âˆˆ N0 = (1,2,...}. Oscillation and...