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Oscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

Advances in Difference Equations (Impact Factor: 0.64). 01/2010; 2010(1-2). DOI: 10.1155/2010/586312
Source: DOAJ

ABSTRACT

We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations (r(t)(x(t)−a(t)x(τ(t)))ΔΔ)Δ+p(t)xγ(δ(t))=0 on a time scale 핋, where γ>0 is a quotient of odd positive integers with r, a, and p real-valued positive rd-continuous functions defined on 핋. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. Some examples are considered to illustrate the main results.

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Available from: Tongxing Li, Jun 01, 2015
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    • "In contrast, the study of oscillation criteria of third order dynamic equations is relatively less. Some interesting results have been obtained concerning the oscillatory and asymptotic behavior of some special cases of the equations (1.1) and (1.2); see [9], [12]. To the best of our knowledge, the oscillatory behavior of (1.1) and (1.2) have not been studied up to now. "
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    ABSTRACT: Some new oscillation criteria for third order neutral nonlinear dynamic equations with distributed deviating arguments on time scales are established. The obtained results extend, improve and correlate many known oscillation results for third order dynamic equations
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    • "r 1 (t)((r 2 (t)(x(t) + a(t)x(τ(t))) ∆ ) ∆ ) γ ) ∆ + p(t)x γ (δ(t)) = 0. Han, Li, Sun, Zhang [14] "
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    ABSTRACT: The aim of this paper is to give oscillation criteria for the third-order quasilinear neutral delay dynamic equation (formula presented) on a time scale T, where 0 < α < γ < ß. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.
    Preview · Article · Jan 2014 · Filomat
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    • "A book on the subject of time scales by M. Bohner and A. Peterson [3] also summarizes and organizes much of the time scale calculus. In the recent years, there has been increasing interest in obtaining sufficient conditions for the oscillation and non-oscillation of solutions of various equations on time-scales; we refer the reader to the papers [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]. T. Candan [15] considered second order nonlinear neutral dynamic equation with distributed deviating arguments "
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    ABSTRACT: The aim of this paper is to give oscillation criteria for the third-order neutral dynamic equations with distributed deviating arguments of the form [r(t)([x(t) + p(t)x(tau(t))](Delta Delta))(gamma)](Delta) + integral(d)(c) f(t, x[phi(t, xi)])Delta xi = 0, where gamma > 0 is the quotient of odd positive integers with r(t) and p(t) real-valued rd-continuous positive functions defined on T. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.
    Preview · Article · Jan 2014 · Filomat
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