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Oscillation and Nonoscillation of Linear Ordinary Differential Equations

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Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

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Abstract

The oscillation and nonoscillation property of solutions of second order linear differential equations is of special interest, and therefore, it has been the subject of many investigations. The interest in second order linear oscillations is due, in a large part, to the fact that many physical systems are modelled by such equations. In this chapter we shall discuss some of the most basic results in the theory of oscillations of linear ordinary differential equations of second order. In Section 2.1, we shall present Sturm and Sturm-Picone comparison theorems which are useful in oscillation theory. In Section 2.2, we shall provide some necessary and sufficient conditions for the nonoscillation as well as some comparison theorems of Sturm’s type. Sufficiency criteria for the nonoscillation are given in Section 2.3. In Section 2.4, we shall establish sufficient conditions for the oscillation of second order differential equations with alternating coefficients. Integral averaging techniques as well as interval criteria for the oscillation are discussed in Section 2.5. In Section 2.6, several criteria for oscillation of linear second order differential equations with integrable coefficients are established. Finally, in Section 2.7 we shall discuss the problems of forced oscillations.

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Authors and Affiliations

  1. Florida Institute of Technology, Melbourne, Florida, USA

    Ravi P. Agarwal

  2. Cairo University, Orman, Giza, Egypt

    Said R. Grace

  3. National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Ravi P. Agarwal
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  2. Said R. Grace
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  3. Donal O’Regan
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© 2002 Springer Science+Business Media Dordrecht

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Agarwal, R.P., Grace, S.R., O’Regan, D. (2002). Oscillation and Nonoscillation of Linear Ordinary Differential Equations. In: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2515-6_2

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  • DOI: https://doi.org/10.1007/978-94-017-2515-6_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6095-2

  • Online ISBN: 978-94-017-2515-6

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