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11. On oscillatory nonlinear fourth-order difference equations with delays

Creator:
Tripathy, Arun K.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, nonlinear, delay, and neutral functional difference equation
Language:
English
Description:
In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form ∆ 2 (r(n)∆2 (y(n) + p(n)y(n − m))) + q(n)G(y(n − k)) = 0 is studied under the assumption ∑∞ n=0 n ⁄ r(n) < ∞. New oscillation criteria have been established which generalize some of the existing results in the literature.
Rights:
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12. On the oscillation of certain class of third-order nonlinear delay differential equations

Creator:
Saker, S. H. and Džurina, J.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
third-order differential equation, oscillation, nonoscillation, and disconjugacy
Language:
English
Description:
In this paper we consider the third-order nonlinear delay differential equation (∗) (a(t) x ′′(t) ) γ ) ′ + q(t)x γ (τ (t)) = 0, t ≥ t0, where a(t), q(t) are positive functions, γ > 0 is a quotient of odd positive integers and the delay function τ (t) 6 t satisfies lim t→∞ τ (t) = ∞. We establish some sufficient conditions which ensure that (∗) is oscillatory or the solutions converge to zero. Our results in the nondelay case extend and improve some known results and in the delay case the results can be applied to new classes of equations which are not covered by the known criteria. Some examples are considered to illustrate the main results.
Rights:
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13. On the oscillation of certain difference equations

Creator:
Grace, S.R. and El-Morshedy, H.A.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, delay difference equations, and forced equations
Language:
English
Description:
In this paper we study the oscillation of the difference equations of the form Δ 2 xn+PnΔxn + f(n, Xn-ff, Δx n-h) = 0, in comparison with certain difference equations of order one whose oscillatory character is known. The results can be applied to the difference equation Δ 2 xn+pnΔxn +q n |x-_g|λ|Δxn -h |μ sgnx„-9 = 0, where A and \i are real constants, λ > 0 and μ ≥ 0.
Rights:
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14. On the oscillation of certain neutral difference equations.

Creator:
Grace, S.R. and Hamedani, G.G.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
nonlinear neutral difference equations, oscillation, asymptotic behavior, oscillatory solutions, and asymptotic behavior of solutions
Language:
English
Description:
Various new criteria for the oscillation of nonlinear neutral difference equations of the form Δi (xn — x n - h) + qn\xn~g\c sgns n -9 =0 , i = 1,2,3 and c > 0, are established.
Rights:
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15. On the oscillation of solutions of third order linear difference equations of neutral type

Creator:
Andruch-Sobiło, Anna and Migda, Małgorzata
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
neutral type difference equation, nonoscillatory solution, asymptotic behavior, oscillation, and third order linear difference equations
Language:
English
Description:
In this note we consider the third order linear difference equations of neutral type (E) ∆ 3 [x(n) − p(n)x(σ(n))] + δq(n)x(τ (n)) = 0, n ∈ N(n0), where δ = ±1, p, q : N(n0) → ℝ+; σ, τ : N(n0) → ℕ, lim n→∞ σ(n) = lim n→∞ τ (n) = ∞. We examine the following two cases: {0 < p(n) ≤ 1, σ(n) = n + k, τ (n) = n + l}, {p(n) > 1, σ(n) = n − k, τ (n) = n − l}, where k, l are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.
Rights:
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16. On the oscillation of Volterra summation equations

Creator:
Thandapani, E. and Ravi, K.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Volterra summation equations, oscillation, and asymptotic behavior
Language:
English
Description:
The asymptotic and oscillatory behavior of solutions of Volterra summation equations yn = pn ± n−1 ∑ s=0 K(n, s)f(s, ys), n ∈ where = {0, 1, 2,...}, are studied. Examples are included to illustrate the results.
Rights:
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17. Oscillation and nonoscillation of second order neutral delay difference equations.

Creator:
Thandapani, Ethiraju and Mahalingam, K.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
neutral delay, difference equation, and oscillation
Language:
English
Description:
Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation \[ \Delta (c_n\Delta (y_n+p_ny_{n-k}))+q_ny_{n+1-m}^\beta =0,\quad n\ge n_0 \] where $k$, $m$ are positive integers and $\beta $ is a ratio of odd positive integers are established, under the condition $\sum _{n=n_0}^{\infty }\frac{1}{c_n}<{\infty }.$.
Rights:
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18. Oscillation in tissue oxygen index during recovery from exercise

Creator:
Yano, T., Afroundeh, R., Shirakawa, K., Lian, C.-S., Shibata, K., Xiao, Z., and Yunoki, T.
Format:
print, bez média, and svazek
Type:
article, články, model:article, and TEXT
Subject:
Fyziologie člověka a srovnávací fyziologie, kmitání, oscillation, tissue oxygen index, recovery from exercise, power spectra density, blood pH, 14, and 612
Language:
English
Description:
It was hypothesized that an oscillation of tissue oxygen index (TOI) determined by near-infrared spectroscopy during recovery from exercise occurs due to feedback control of adenosine triphosphate and that frequency of the oscillation is affected by blood pH. In order to examine these hypotheses, we aimed 1) to determine whether there is an oscillation of TOI during recovery from exercise and 2) to determine the effect of blood pH on frequency of the oscillation of TOI. Three exercises were performed with exercise intensities of 30 % and 70 % peak oxygen uptake (Vo2peak) for 12 min and with exercise intensity of 70 % Vo2peak for 30 s. TOI during recovery from the exercise was analyzed by fast Fourier transform in order to obtain power spectra density (PSD). There was a significant difference in the frequency at which maximal PSD of TOI appeared (Fmax) between the exercises with 70 % Vo2peak for 12 min (0.0039±0 Hz) and for 30 s (0.0061±0.0028 Hz). However, there was no significant difference in Fmax between the exercises with 30 % (0.0043±0.0013 Hz) and with 70 % Vo2peak for 12 min despite differences in blood pH and blood lactate from the warmed fingertips. It is concluded that there was an oscillation in TOI during recovery from the three exercises. It was not clearly shown that there was an effect of blood pH on Fmax., T. Yano, R. Afroundeh, K. Shirakawa, C.-S. Lian, K. Shibata, Z. Xiao, T. Yunoki., and Obsahuje bibliografii
Rights:
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19. Oscillation of a nonlinear difference equation with several delays

Creator:
Luo, X. N., Zhou, Yong, and Li, C. F.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
nonlinear difference equtions, oscillation, eventually positive solutions, and characteristic equation
Language:
English
Description:
In this paper we consider the nonlinear difference equation with several delays (axn+1 + bxn) k − (cxn) k + ∑m i=1 pi(n)x k n−σi = 0 where a, b, c ∈ (0, ∞), k = q/r, q, r are positive odd integers, m, σi are positive integers, {pi(n)}, i = 1, 2, . . . , m, is a real sequence with pi(n) ≥ 0 for all large n, and lim inf n→∞ pi(n) = pi < ∞, i = 1, 2, . . . , m. Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.
Rights:
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20. Oscillation of certain difference equations

Creator:
Grace, Said R.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math, equations, and oscillation
Language:
English
Description:
Some new criteria for the oscillation of difference equations of the form \[ \Delta ^2 x_n - p_n \Delta x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm sgn}x_{g_n} = 0 \] and \[ \Delta ^i x_n + p_n \Delta ^{i-1} x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm sgn}x_{g_n} = 0, \ i = 2,3, \] are established.
Rights:
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