Vol. 51, No. 1, 1974

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Oscillation and nonoscillation criteria for some self-adjoint even order linear differential operators

Roger T. Lewis

Vol. 51 (1974), No. 1, 221–234
Abstract

Oscillation and nonoscillation results are presented for the operator

       ∑n    n−k    (n−k)(n−k)
L2ny =   (− 1)  (pky    )
k=0

where p0(x) > 0 on (0,) and for k = 0,1,,n,pk is a realvalued, n k times differentiable function on (0,). Also, y is an element of the set of all real-valued, 2n-fold continuously differentiable, finite functions on (0,).

In particular, a nonoscillation result is given for L2n without sign restrictions on the coefficients. Oscillation results are given for L4 without the requirement that p1 be negative for large x. Finally, the oscillation of

L  y = (− 1)n(ry(n))(n) + py
2n

is considered for r(x) not necessarily bounded.

Mathematical Subject Classification 2000
Primary: 34C10
Milestones
Received: 18 December 1972
Revised: 15 June 1973
Published: 1 March 1974
Authors
Roger T. Lewis