International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 105-109
doi:10.1155/S0161171286000133

Comparison theorems for fourth order differential equations

Garret J. Etgen1 and Willie E. Taylor Jr.2

1Department of Mathematics, University of Houston, University Park, Houston 77004, Texas, USA
2Department of Mathematics, Texas Southern University, Houston 77004, Texas, USA

Received 23 April 1984; Revised 1 August 1985

Copyright © 1986 Garret J. Etgen and Willie E. Taylor. 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.

Abstract

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equations yiv−p(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.