An Oscillation Condition for Differential Equations of Arbitrary Order

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 1981Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 82, page 548 (issn: 0002-9939,

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Authors: Trench, William F.;

doi: 10.2307/2043769 , 10.1090/s0002-9939-1981-0614876-4

An Oscillation Condition for Differential Equations of Arbitrary Order

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Abstract

In separate papers, D. L. Lovelady has related oscillation of solutions of certain linear differential equations of odd order ⩾ 3 \geqslant 3 and even order ⩾ 4 \geqslant 4 to oscillation of an associated second order equation. This paper presents a unified proof of Lovelady’s results for equations of arbitrary order ⩾ 3 \geqslant 3 . The results are somewhat more detailed and the equations need not be linear.

Keywords

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, extendible solution

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