5,473 research outputs found

    Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

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    2000 Mathematics Subject Classification: 34C10, 34C15.It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term (a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0, where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line and can be applied to extreme cases such as ∫t0∞ q(t) dt = − ∞. Our results are illustrated with an example

    Nonlinear structural vibrations by the linear acceleration method

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    Numerical integration method for calculating dynamic response of nonlinear elastic structure

    Interval oscillation theorems for asecond-order linear differential equation

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    AbstractInterval oscillation criteria are given for the forced second-order linear differential equation Ly(t) = (p(t)y′)′ + q(t)y = ƒ(t), tε (0, ∞), where p, q, ƒ are locally integrable functions and p(t) > 0, for t > 0. No restriction is imposed on ƒ(t) to be the second derivative of an oscillatory function as assumed by Kartsatos [1). Our results also allow both q and f to change sign in the neighborhood at infinity. In particular, we show that all solutions of y″ + c(sin t)y = tβ cos t with β ≥ 0 are oscillatory, for c ≥ 1.3448. This improves an estimate given by Nasr [2] for the linear equation

    Integral averaging technique for the interval oscillation criteria of certain second-order nonlinear differential equations

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    AbstractWe present new interval oscillation criteria related to integral averaging technique for certain classes of second-order nonlinear differential equations which are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line. They generalize and improve some known results. Examples are also given to illustrate the importance of our results

    Periodically Forced Nonlinear Oscillators With Hysteretic Damping

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    We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small quadratic stiffness term in the constitutive equation and construct the periodic solution of the problem by a systematic perturbation method, neglecting transient terms as tt\rightarrow \infty. We then repeat the analysis replacing the quadratic by a cubic term, which does not allow the solutions to escape to infinity. In both cases, we examine the dependence of the amplitude of the periodic solution on the different parameters of the model and discuss the differences with the linear model. We point out certain undesirable features of the solutions, which have also been alluded to in the literature for the linear Bishop's model, but persist in the nonlinear case as well. Finally, we discuss an alternative hysteretic damping oscillator model first proposed by Reid [2], which appears to be free from these difficulties and exhibits remarkably rich dynamical properties when extended in the nonlinear regime.Comment: Accepted for publication in the Journal of Computational and Nonlinear Dynamic

    Asymptotic solutions of forced nonlinear second order differential equations and their extensions

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    Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented

    Oscillation of a time fractional partial differential equation

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    We consider a time fractional partial differential equation subject to the Neumann boundary condition. Several sufficient conditions are established for oscillation of solutions of such equation by using the integral averaging method and a generalized Riccati technique. The main results are illustrated by examples
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