On The Bounded Oscillation of Certain Second-order Nonlinear Neutral Delay Dynamic Equations with Oscillating Coefficients
نویسندگان
چکیده
Received: November 24, 2010 Accepted: December 10, 2010 doi:10.5539/jmr.v3n2p193 This work was supported by the Science and Technology Program of Hunan Province of P. R. China (Grant No. 2010FJ6021). Abstract We investigate the bounded oscillation of the second-order nonlinear neutral delay dynamic equation with oscillating coefficients ( r(t) ∣∣∣∣[x(t) + p(t)x(τ(t))]Δ∣∣∣∣α−1[x(t) + p(t)x(τ(t))]Δ)Δ + q(t)|x(t)|β−1x(t) = 0 on an arbitrary time scale T, where p is an oscillating function defined on T and α, β > 0 are constants, and obtain several sufficient conditions for the oscillation of all bounded solutions of the equation when β > α, β = α and β < α, respectively. Our results extend and complement some known results where p(t) ≡ 0 and α, β are quotients of odd positive integers.
منابع مشابه
Bounded Oscillation of Second-Order Half-Linear Neutral Delay Dynamic Equations
In this paper, we deal with the oscillation of bounded solutions of a class of second-order half-linear neutral delay dynamic equations with an oscillating coefficient on a time scale. We establish several oscillation criteria for all bounded solutions of the equations by employing a generalized Riccati technique and an integral averaging technique. The results obtained here extend and compleme...
متن کاملNonlinear oscillation of certain third-order neutral differential equation with distributed delay
The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...
متن کاملUncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation
In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...
متن کاملOscillation of Nonlinear Neutral Type Dynamic Equations
This paper is intended to study the oscillatory behaviour of solutions of the higher order nonlinear neutral type functional dynamic equation with oscillating coefficients of the following form: [y(t) + p(t)y (τ(t))] n + m ∑ i=1 qi(t)fi (y (φi(t))) = s(t) where n ≥ 2. We obtain sufficient conditions for oscillatory behaviour of its solutions. Our results complement the oscillation results for n...
متن کاملOscillation theorems for second-order nonlinear neutral dynamic equations with variable delays and damping
In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples. Key...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011