• Title/Summary/Keyword: asymptotic behaviour

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ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS

  • Simeonov, P.S.;Bainov, D.D.
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.1-14
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    • 1994
  • In the recent several years the theory of impulsive differential equations has made a rapid progress (see [1] and [2] and the references there). The questions of stability and periodicity of the solutions of these equations have been elaborated in sufficient details while their asymptotic behaviour has been little studied. In the present paper the asymptotic behaviour of the solutions of linear impulsive differential equations is investigated, generalizing the results of J. W. Macki and J.S. Muldowney, 1970 [3], related to ordinary differential equations without impulses.

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ASYMPTOTIC BEHAVIOUR FOR SEMILINEAR DIFFERENTIAL SYSTEMS

  • Song, Se-Mok;Im, Dong-Man;Lee, Gi-Soo
    • Journal of applied mathematics & informatics
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    • v.15 no.1_2
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    • pp.527-537
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    • 2004
  • This paper deals with the asymptotic behaviour for the semi-linear differential systems x' (t) = A(t)χ + f(t, x). We give a detailed proof of known generalization of Coppel's result about the above mentioned system.

OSCILLATORY BEHAVIOUR OF SOLUTIONS OF y"+P(x)y=f(x)

  • Zaghrout, A.A.S.;Ragab, A.A.
    • Kyungpook Mathematical Journal
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    • v.27 no.1
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    • pp.7-13
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    • 1987
  • This paper is a study of the oscillatory and asymptotic behaviour of solutions of the second order nonhomogeneous linear differential equation y"+P(x)y=f(x), and the associated homogeneous equation. Conditions are determined, under which the nonhomogeneous equation is oscillatory if and only if the homogeneous equation is oscillatory.

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