Vol. 92, No. 2, 1981

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Oscillation criteria for general linear ordinary differential equations

Takaŝi Kusano and Manabu Naito

Vol. 92 (1981), No. 2, 345–355
Abstract

Lovelady has recently proved the following oscillation theorem.

Theorem. Let n 4 be even and q : [a,) (0,) be continuous. If tn2q(t)dt < and the second order equation

d2z      1   ∫ ∞      n−3
dt2 + ((n−-3)!   (s − t)   q(s)ds)z = 0
t

is oscillatory, then the n-th order equation

x(n) + q(t)x = 0

is oscillatory.

In this paper the above theorem will be extended to a class of differential equations of the form

-1---d --1----d⋅⋅⋅-d--1- d--x-- +q(t)x = 0.
pn(t)dt pn−1(t)dt   dtp1(t)dtp0(t)

Mathematical Subject Classification 2000
Primary: 34C10
Milestones
Received: 3 October 1979
Published: 1 February 1981
Authors
Takaŝi Kusano
Manabu Naito