Comparison theorems for fourth order differential equations
Garret J. Etgen1and Willie E. Taylor2
Received23 Apr 1984
Revised01 Aug 1985
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.