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Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations pp 376–456Cite as

Oscillation Theory for Sublinear Differential Equations

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Abstract

In this chapter we shall present oscillation and nonoscillation criteria for all solutions of second order nonlinear differential equations of sublinear type with alternating coefficients. In Section 5.1, our sublinear oscillation results involve integrals and weighted integrals of the alternating coefficients. In some results we employ integral averaging techniques. In Section 5.2, we impose some additional conditions on the sublinear term which allow us to proceed further and extend and improve several known theorems in the literature. In fact, we make an asymptotic study which results in new oscillation criteria. Section 5.3 provides some new linearized oscillation results for second order sublinear differential equations. In Section 5.4, we shall present criteria for the nonoscillation of sublinear Emden-Fowler type equations. In Section 5.5, we compare the oscillatory behavior of certain nonlinear equations with the related half-linear differential equations. Here oscillation of general nonlinear differential equations is also discussed.

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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 Theory for Sublinear 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_5

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  • DOI: https://doi.org/10.1007/978-94-017-2515-6_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6095-2

  • Online ISBN: 978-94-017-2515-6

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