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Further Results on the Oscillation of Differential Equations

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

Author

Listed:
  • Ravi P. Agarwal

    (Florida Institute of Technology)

  • Said R. Grace

    (Cairo University)

  • Donal O’Regan

    (National University of Ireland)

Abstract

In this chapter we shall discuss some techniques which are different than those employed in the previous chapters to obtain oscillatory criteria for differential equations. In Section 6.1 we shall present oscillation and nonoscillation theorems for nonlinear second order differential equations by using the method of Olech, Opial and Wazewski. Section 6.2 is concerned with the oscillation of half-linear second order differential equations by employing the variational inequality given in Lemma 3.2.6. In Section 6.3 we shall begin with some preliminaries of Liapunov functions, and then apply Liapunov second method to obtain criteria for the oscillation of second order nonlinear equations.

Suggested Citation

  • Ravi P. Agarwal & Said R. Grace & Donal O’Regan, 2002. "Further Results on the Oscillation of Differential Equations," Springer Books, in: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, chapter 0, pages 457-490, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2515-6_6
    DOI: 10.1007/978-94-017-2515-6_6
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