• 제목/요약/키워드: Nonlinear differential equations

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INTERVAL OSCILLATION THEOREMS FOR SECOND-ORDER DIFFERENTIAL EQUATIONS

  • Bin, Zheng
    • Journal of applied mathematics & informatics
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    • 제27권3_4호
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    • pp.581-589
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    • 2009
  • In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term and forcing term: $$(r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+q(t)f(x(t))=0$$. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity. And, as a consequence, our results apply to wider classes of nonlinear differential equations. Some illustrative examples are considered.

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ON THE STABILITY AND INSTABILITY OF A CLASS OF NONLINEAR NONAUTONOMOUS ORDINARY DIFFERENTIAI, EQUATIONS

  • Sen, M.DeLa
    • Bulletin of the Korean Mathematical Society
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    • 제40권2호
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    • pp.243-251
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    • 2003
  • This note Presents sufficient conditions for Lyapunov's stability and instability of a class of nonlinear nonautonomous second-order ordinary differential equations. Such a class includes as particular cases a remarkably large number of differential equations with specific physical applications. Two successive nonlinear transformations are applied to the original differential equation in order to convert it into a more convenient form for stability analysis purposes. The obtained stability / instability conditions depend closely on the parameterization of the original differential equation.

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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    • 제11권1_2호
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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.

On asymptotic stability in nonlinear differential system

  • An, Jeong-Hyang
    • Journal of the Korean Data and Information Science Society
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    • 제21권3호
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    • pp.597-603
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    • 2010
  • We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.

DECOMPOSITION METHOD FOR SOLVING NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

  • KAMEL AL-KHALED;ALLAN FATHI
    • Journal of applied mathematics & informatics
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    • 제19권1_2호
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    • pp.415-425
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    • 2005
  • This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method.

ENHANCED SEMI-ANALYTIC METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

  • JANG, BONGSOO;KIM, HYUNJU
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제23권4호
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    • pp.283-300
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    • 2019
  • In this paper, we propose a new semi-analytic approach based on the generalized Taylor series for solving nonlinear differential equations of fractional order. Assuming the solution is expanded as the generalized Taylor series, the coefficients of the series can be computed by solving the corresponding recursive relation of the coefficients which is generated by the given problem. This method is called the generalized differential transform method(GDTM). In several literatures the standard GDTM was applied in each sub-domain to obtain an accurate approximation. As noticed in [19], however, a direct application of the GDTM in each sub-domain loses a term of memory which causes an inaccurate approximation. In this work, we derive a new recursive relation of the coefficients that reflects an effect of memory. Several illustrative examples are demonstrated to show the effectiveness of the proposed method. It is shown that the proposed method is robust and accurate for solving nonlinear differential equations of fractional order.