International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 391272 | https://doi.org/10.1155/S0161171286000133

Garret J. Etgen, Willie E. Taylor, "Comparison theorems for fourth order differential equations", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 391272, 5 pages, 1986. https://doi.org/10.1155/S0161171286000133

Comparison theorems for fourth order differential equations

Received23 Apr 1984
Revised01 Aug 1985

Abstract

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equations yivp(x)y=0 and yiv+p(x)y=0, where p is a positive, continuous function defined on [0,). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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