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Oscillation Criteria for Second Order Nonlinear Differential Equations Involving Integral Averages

Published online by Cambridge University Press:  20 November 2018

James S. W. Wong
James S. W. Wong*
Affiliation:
Chinney Investments Limited 1218 Swire House Hong Kong Department of Mathematics University of Science and Technology Hong Kong
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Abstract

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Consider the second order nonlinear differential equation

y" + a(t)f(y) = 0

where a(t) ∈ C[0,∞),f(y) GC1 (-∞, ∞),ƒ'(y) ≥ 0 and yf(y) > 0 for y ≠ 0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the prototype nonlinear function f(y) = |γ|γ sgny with γ > 1 and 0 < γ < 1 known as the Emden-Fowler case. The coefficient a(t) is allowed to be negative for arbitrarily large values of t. Oscillation criteria involving integral averages of a(t) due to Wintner, Hartman, and recently Butler, Erbe and Mingarelli for the linear equation are shown to remain valid for the general equation, subject to certain nonlinear conditions on f(y). In particular, these results are therefore valid for the Emden-Fowler equation.

Keywords

34C1034C15second ordernonlinearordinary differential equationsoscillationasymptotic behavior
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 1094 - 1103
Copyright
Copyright © Canadian Mathematical Society 1993

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