Samir H Saker

Publications (116) View all

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  Available from: Samir H Saker

  Dataset: Submitted

  Elmetwally M. Elabbasy, Taher S. Hassan, Samir H. Saker
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  Available from: Metwally Elabbasy

  Article: Oscillation of nonlinear neutral delay differential Equations

  Elmetwally M. Elabbasy, Taher S. Hassan, Samir H. Saker
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  ABSTRACT: In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equations. Several new sufficient conditions which ensure that all solutions are oscillatory are given. The obtained results extend and improve several known results in the literature. Some examples are considered to illustrate the main results.
  Journal of Applied Mathematics and Computing 04/2012; 21(1):99-118.
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  Article: Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function

  Samir H. Saker
  Journal of Inequalities and Applications. 01/2010;
• Article: Oscillation theorems for second-order nonlinear neutral delay dynamic equations on time scales

  Samir H. Saker, Donal O’regan, Ravi P. Agarwal
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  ABSTRACT: By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation $ [r(t)[y(t) + p(t)y(\tau (t))]^\Delta ]^\Delta + q(t)f(y(\delta (t))) = 0 $ [r(t)[y(t) + p(t)y(\tau (t))]^\Delta ]^\Delta + q(t)f(y(\delta (t))) = 0 , on a time scale $ \mathbb{T} $ \mathbb{T} . The results improve some oscillation results for neutral delay dynamic equations and in the special case when $ \mathbb{T} $ \mathbb{T} = ℝ our results cover and improve the oscillation results for second-order neutral delay differential equations established by Li and Liu [Canad. J. Math., 48 (1996), 871–886]. When $ \mathbb{T} $ \mathbb{T} = ℕ, our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh [Comp. Math. Appl., 36 (1998), 123–132]. When $ \mathbb{T} $ \mathbb{T} =hℕ, $ \mathbb{T} $ \mathbb{T} = {t: t = q k , k ∈ ℕ, q > 1}, $ \mathbb{T} $ \mathbb{T} = ℕ2 = {t 2: t ∈ ℕ}, $ \mathbb{T} $ \mathbb{T} = $ \mathbb{T}_n $ \mathbb{T}_n = {t n = Σ k=1 n $ \tfrac{1} {k} $ \tfrac{1} {k} , n ∈ ℕ0}, $ \mathbb{T} $ \mathbb{T} ={t 2: t ∈ ℕ}, $ \mathbb{T} $ \mathbb{T} = {√n: n ∈ ℕ0} and $ \mathbb{T} $ \mathbb{T} ={$ \sqrt[3]{n} $ \sqrt[3]{n} : n ∈ ℕ0} our results are essentially new. Some examples illustrating our main results are given.
  Acta Mathematica Sinica 08/2008; 24(9):1409-1432. · 0.47 Impact Factor
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  Article: Oscillation criteria for sublinear half-linear delay dynamic equations

  Lynn Erbe, Taher S Hassan, Allan Peterson, Samir H Saker
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  ABSTRACT: This paper is concerned with oscillation of the second-order half-linear delay dynamic equation (r(t)(x ∆) γ) ∆ + p(t)x γ (τ (t)) = 0, on a time scale T where 0 < γ ≤ 1 is the quotient of odd positive integers, p : T → [0, ∞), and τ : T → T are positive rd-continuous functions, r(t) is a positive and (delta) differentiable function, τ (t) ≤ t, and lim t→∞ τ (t) = ∞. We es-tablish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our results in the special cases when T = R and T = N involve and improve some oscillation results for second-order differential and dif-ference equations; and when T = hN, T = q N 0 and T = N 2 our oscillation results are essentially new. Some examples illustrating the importance of our results are also included.
  International Journal of Difference Equations ISSN0973. 01/2008;