Agacik Zafer

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f t, x q t Φα x ∑n i 1qi t Φβi x , Φ∗ u |u|∗−1u, where t0,∞ T is a time scale interval with t0 ∈ T, the functions r, q, qi, e : t0,∞ T → R are right-dense continuouswith r > 0, σ is the forward jump operator, x t : x σ t , and β1 > · · · > βm > α > βm 1 > · · · βn > 0. All results obtained are new even for T R and T Z. In the special case when T R and α 1(More)
i=1 pi(t)Φβi (x(τi(t))) = e(t), t ∈ [t0,∞)T where T is a time scale, t0 ∈ T a fixed number; [t0,∞)T is a time scale interval; Φ∗(u) = |u|∗−1u; the functions r, pi, e : [t0,∞)T → R are right-dense continuous with r > 0 nondecreasing; τk : T → T are nondecreasing right-dense continuous with τk(t) ≤ t , limt→∞ τk(t) = ∞; and the exponents satisfy β1 > · · · >(More)
By means of Riccati transformation technique, we establish some new oscillation criteria for the third-order nonlinear delay dynamic equations x 3 (t) + p(t)x(τ(t)) = 0 on a time scale T unbounded above, here γ > 0 is a quotient of odd positive integers with p real-valued positive rd-continuous function defined on T. Three examples are given to illustrate(More)
To cite this Article Anderson, Douglas R. and Zafer, A.(2010) 'Interval criteria for second-order super-half-linear functional dynamic equations with delay and advance arguments', This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing,(More)