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Abstract  

If X is a topological space and (Y,d) is a metric space, then for each locally bounded function f : XY all possible superpositions of oscillations and quasi-oscillations give at most eight functions.

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Acta Physiologica Hungarica
Authors: T. Yano, R. Afroundeh, R. Yamanaka, T. Arimitsu, C.S. Lian, K. Shirakawa, and T. Yunoki

Iotti S, Borsari M, Bendahan D: Oscillations in energy metabolism. Biochimica et Biophysica Acta 1797, 1353–1361 (2010) Bendahan D. Oscillations in energy metabolism Biochimica et Biophysica Acta 2010

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References [1] Kamo , K. , Usami , H. 2002 Oscillation theorems for fourth-order quasilinear ordinary differential equations Studia Sci. Math. Hungar. 39 385 – 406

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References [1] Agarwal , R. P. , Shien , S. L. , Yeh , C. C. 1997 Oscillation criteria for second order retarded differential equations Math. Comput. Modelling 26 1 – 11 10

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Acta Physiologica Hungarica
Authors: T. Yano, C. Lian, T. Arimitsu, R. Yamanaka, R. Afroundeh, K. Shirakawa, and T. Yunoki

young and older adult humans J. Appl. Physiol. 2004 97 998 1005 Gooch VD, Parker L: Adenine nucleotide control of heart mitochondrial oscillations. Biochim. Biophys. Acta 245, 17–20 (1971

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metabolism ( 22 ). Furthermore, it was pointed out by referring to Richard’s oscillation model ( 15 ) that the oscillation of TOI was caused by feedback of adenosine triphosphate (ATP) to oxidative phosphorylation ( 22 ). Recently, it has been reported that

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Summary  

Using the integral average method, we give some new oscillation criteria for the second order differential equation with damped term  (a(t)Ψ(x(t))K(x'(t)))'+p(t)K(x'(t))+q(t)f(x(t))=0, t≧t0. These results improve and generalize the oscillation criteria in[1], because they eliminate both the differentiability of p(t) and the sign of p(t), q(t). As a consequence, improvements of Sobol's type oscillation criteria are obtained.

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Abstract  

We present new oscillation criteria for the second order nonlinear neutral delay differential equation [y(t)-py(t-τ)]''+ q(t)y λ (g(t)) sgn y(g(t)) = 0, tt 0. Our results solve an open problem posed by James S.W . Wong [24]. The relevance of our results becomes clear due to a carefully selected example.

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Abstract  

This paper is concerned with a class of even order nonlinear damped differential equations

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\begin{gathered} {\text{ }}x^{(n)} (t) + p(t)x^{(n - 1)} (t) \hfill \\ + f\left( {t,x[\tau _{01} (t)],...,x[\tau _{0m} (t)],...,x^{(n - 1)} [\tau _{n - 11} (t)],...,x^{{\text{(n - 1)}}} [\tau _{n - 1n} (t)]} \right) = 0 \hfill \\ \end{gathered}$$ \end{document}
where n is even and tt 0. By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results.

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Abstract  

We present some criteria for the oscillation of the second order nonlinear differential equation [a(t)ψ(x(t))x'(t)]' + p(t)x'(t) + q(t)f (x(t)) =0, tt 0> 0 with damping where aC 1 ([t 0,∞)) is a nonnegative function, p, q∈ C([t 0,∞)) are allowed to change sign on [t 0,∞), ψ, f∈C(R) with ψ(x) ≠ 0, xf(x)/ψ(x) > 0 for x≠ 0, and ψ, f have continuous derivatives on R{0} with [f(x) / ψ(x)]' ≧ 0 for x≠ 0. This criteria are obtained by using a general class of the parameter functions H(t,s) in the averaging techniques. An essential feature of the proved results is that the assumption of positivity of the function ψ(x) is not required. Consequently, the obtained criteria cover new classes of equations to which known results do not apply.

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