COMPARISON THEOREMS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS

ABSTRACT. This paper establishes an apparently overlooked relationship between the iv yiVp’air of fourth order line,r equations y p(x)y 0 and + p(x)y 0, where p is, positive, continuous function defined on [O,m). 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. KEY WORDS AND PHRASES. Oscillatory solutions; nonoscillatory solutions; fourth order linear differential equations. 1980 MATHEMATICS SUBJECT CLASSIFICATION CODE. 34CI0 I. INTRODUCTION. This note is concerned with the pair of fourth order linear differential equations ivy p(x)y 0 (I.I) iv y + p(x)y 0 (1.2