Oscillation Theory for Sublinear 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 5 in Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, 2002, pp 376-456 from Springer

Abstract: 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.

Keywords: Nonlinear Differential Equation; Oscillation Theory; Nonoscillatory Solution; Oscillation Criterion; Oscillation Theorem (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2515-6_5

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DOI: 10.1007/978-94-017-2515-6_5

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