Further Results on the Oscillation of Differential Equations

Ravi P. Agarwal, Said R. Grace and Donal O’Regan
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Ravi P. Agarwal: Florida Institute of Technology
Said R. Grace: Cairo University
Donal O’Regan: National University of Ireland

Chapter Chapter 6 in Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, 2002, pp 457-490 from Springer

Abstract: 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.

Date: 2002
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DOI: 10.1007/978-94-017-2515-6_6

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