• Title/Summary/Keyword: Nonlinear Oscillation

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INTERVAL OSCILLATION CRITERIA FOR A SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

  • Zhang, Cun-Hua
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1165-1176
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    • 2009
  • This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

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OSCILATION AND STABILITY OF NONLINEAR NEUTRAL IMPULSIVE DELAY DIFFERENTIAL EQUATIONS

  • Duan, Yongrui;Tian, Peng;Zhang, Shunian
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.243-253
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    • 2003
  • In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equations are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.

Oscillation of Second Order Nonlinear Elliptic Differential Equations

  • Xu, Zhiting
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.65-77
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    • 2006
  • By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping $$\sum_{i,j=1}^{N}D_i[a_{ij}(x)D_iy]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0$$ are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.

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The Prediction of Self-Excited Oscillation of a Fuzzy Control System Based on the Describing Function - Static Case (묘사함수를 이용한 퍼지 제어 시스템의 자기진동 현상의 예측 - 정적 경우)

  • 김은태;노흥식;김동연;박민용
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.35C no.3
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    • pp.90-96
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    • 1998
  • The self-excited oscillation is the phenomenon which can be observed in the systems composed of nonlinear elements. The phenomenon is of fundamental importance in nonlinear systems and, as far as the design of a nonlinear system is concerned, it should be considered along with the stability analysis. In this paper, the oscillation of a system controlled by a static nonlinear fuzzy controller is theoretically addressed. First, the describing functionof a static fuzzy controller is derived and then, based on the derived describing function, self-excited oscillation of the system controlled by a static fuzzy controller is predicted. To obtain the describing function of the static fuzzy controller, a simple struture is assumed for the fuzzy controller. Finally, computer simulation is included to show an example where the describing function given in the paper is used to predict the self-excited oscillation of a fuzzy-control system.

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ON THE OSCILLATION OF SECOND-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

  • Zhang, Quanxin;Sogn, Xia;Gao, Li
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.219-234
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    • 2012
  • By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criterion for the second-order nonlinear delay dynamic equations $$(a(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+q(t)f(x({\tau}(t)))=0$$ on a time scale $\mathbb{T}$, here ${\gamma}{\geq}1$ is the ratio of two positive odd integers with $a$ and $q$ real-valued positive right-dense continuous functions defined on $\mathbb{T}$. Our results not only extend and improve some known results, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

OSCILLATION THEOREMS FOR CERTAIN SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

  • Sun, Yibing;Han, Zhenlai;Zhao, Ping;Sun, Ying
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1557-1569
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    • 2011
  • In this paper, we consider the oscillation of the following certain second order nonlinear differential equations $(r(t)(x^{\prime}(t))^{\alpha})^{\prime}+q(t)x^{\beta}(t)=0$>, where ${\alpha}$ and ${\beta}$ are ratios of positive odd integers. New oscillation theorems are established, which are based on a class of new functions ${\Phi}={\Phi}(t,s,l)$ defined in the sequel. Also, we establish some interval oscillation criteria for this equation.