具有振动系数的二阶非线性中立型时滞动力方程的有界振动性

Abstract

Abstract:

In this paper, we investigate the oscillation of bounded solutions of second-order nonlinear neutral delay dynamic equation with oscillating coefficients of the form
(r(t)([y(t)+p(t)y(τ(t))]^Δ)^α)^Δ+f(t, y(δ(t)))=0
on an arbitrary time scale T, where p is an oscillating function defined on T and α>0 is a quotient of odd positive integers. We get some sufficient conditions for the oscillation of all bounded solutions of the equation by developing a Riccati transformation technique. The obtained results extend and complement some known results in which p(t)≥0 for t∈T is required. Several examples are presented to illustrate our main results.

Key words: Bounded oscillation, Second-order nonlinear neutral delay dynamic equation, Oscillating coefficient, Time scale, Riccati transformation

CLC Number:

39A10

CHEN Da-Xue. Bounded Oscillation for Second-order Nonlinear Neutral Delay Dynamic Equations with Oscillating Coefficients[J].Acta mathematica scientia,Series A, 2013, 33(1): 98-113.

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Bounded Oscillation for Second-order Nonlinear Neutral Delay Dynamic Equations with Oscillating Coefficients

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