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Journal of the London Mathematical Society 1996 53(1):118-126; doi:10.1112/jlms/53.1.118
© 1996 by London Mathematical Society
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© The London Mathematical Society

A Comparison Theorem for a Second Order Linear Quasi-Differential Equation

J. G. O'Hara

Department of Mathematics, University of Botswana Private Bag 0022, Gaborone, Botswana

Received 13 November 1992. Revision received 24 January 1994. Revision received 13 June 1994.

We are concerned with the non-oscillatory behaviour of a second order linear quasi-differential equation defined a.e. over a half-line. More particularly given that (py')' + qy = 0 is non-oscillatory we show that by writing q in a form which is amenable to further analysis we can generalise Sturm's comparison theorem.


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