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Oscillation and asymptotic behavior of second order neutral differential equations
Annali di Matematica Pura ed Applicata, 1987The authors consider the following second order differential equation \[ (1)\quad \frac{d^ 2}{dt^ 2}[y(t)+P(t)y(t-\tau)]+Q(t)y(t- \sigma)=0,\quad t\geq t_ 0,\quad \tau,\sigma \geq 0 \] with \(P,Q\in C([t_ 0,\infty],{\mathbb{R}})\), where the highest derivate of the unknown function appears both with delays \(\tau\) and \(\sigma\) in some terms and ...
Grammatikopoulos, M. K. +2 more
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Oscillation and asymptotic behavior of a system of linear difference equations
Applicable Analysis, 1992We obtain necessary and sufficient conditions for the oscillation of all solutions of the system of difference equations where p is a real number. We also investigate the asymptotic behavior of all solutions.
D. A. Georgiou, G. Ladas, P. N. Vlahos
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Oscillation and asymptotic behavior of neutral differential equations with deviating arguments
Applicable Analysis, 1986Consider the neutral differential equation where q≠0, p, τ, and σ are real numbers. Let y(t) be a nonoscillatory solution of Eq. (1). Then limtt→∞y(t) is determined for all cases, except: . Two conjectures (as well as evidence indicating their possible validity) are given to cover the missing cases i), ii), and iii).
M. K. Grammatikopoulos +2 more
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OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOME SECOND ORDER RETARDED DIFFERENTIAL EQUATIONS
Acta Mathematica Scientia, 1991Abstract In this paper, we consider the following second order retarded differential equations x ″ ( t ) + c x ′ ( t ) = q x ( t - σ ) = ; x ( t - δ ) x ″ ( t ) + p ( t ) x ( t - τ ) = 0 We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the
Mingxin Wang, Qin Zhang
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The asymptotic behavior of an infinite system of connected oscillators
Mathematical Notes, 1993Suppose on a probability space \((\Omega, \sigma, P)\) an increasing flow \((F_t)_{t \geq 0}\) of \(\sigma\)-algebras is given. We consider the infinite-dimensional diffusion process \(\xi(t) = (\xi (t,x), z \in \mathbb{Z}^\nu)\), defined by the system of Itô equations \[ d \xi (t,z) = w_z dt + dW(t,x), \tag{2} \] where \(W(t,z)\), \(t \geq 0\), are ...
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Oscillations and asymptotic behavior of first-order neutral delay differential equations
Applicable Analysis, 1988Consider the neutral delay differential equation [display math001] In this paper we are concerned with the asymptotic behavior and the oscillatory nature of solutions of Eq. (1).
E. A. Grove, G. Ladas, S.W. Schultz
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Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agarwal, Ravi P. +4 more
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Oscillation and Asymptotic Behavior of Solutions of Third order Differential Delay Equations
SIAM Journal on Mathematical Analysis, 1976In this paper we introduce comparison techniques for studying the oscillatory and asymptotic behavior of solutions of third order differential equations with retarded argument. This allows the use of “Kneser-type”, as well as integral, criteria for deciding the behavior of the solutions.
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Mathematische Nachrichten, 1988
The authors investigate the nonlinear second order differential inequality \[ x(t)[\frac{d}{dt}(a(t)\frac{dx(t)}{dt})+q(t)f(x(g(t)))]\leq 0,\quad t\geq t_ 0, \] where a, q, g, f are given continuous functions and g(t)\(\leq t\), \(dg(t)/dt\geq 0,\) \(t\geq t_ 0\), \(\lim_{t\to \infty}g(t)=\infty,\) \(xf(x)>0\), \(x\neq 0\).
Grace, S. R., Lalli, B. S.
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The authors investigate the nonlinear second order differential inequality \[ x(t)[\frac{d}{dt}(a(t)\frac{dx(t)}{dt})+q(t)f(x(g(t)))]\leq 0,\quad t\geq t_ 0, \] where a, q, g, f are given continuous functions and g(t)\(\leq t\), \(dg(t)/dt\geq 0,\) \(t\geq t_ 0\), \(\lim_{t\to \infty}g(t)=\infty,\) \(xf(x)>0\), \(x\neq 0\).
Grace, S. R., Lalli, B. S.
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Asymptotic Behavior of the Correlation Function of a Randomly Modulated Oscillator
Journal of the Physical Society of Japan, 1967Asymptotic behavior of the correlation function of a randomly modulated oscillator is examined. When the frequency modulation is a stationary stochastic process such as a Gaussian process or a Poisson impulse, it is proved that the correlation function approaches asymptotically to a simple exponential function, the coefficients of which can be given in
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