Vol. 67, No. 2, 1976

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Nth order oscillations with middle terms of order N 2

Athanassios G. Kartsatos

Vol. 67 (1976), No. 2, 477–488
Abstract

Equations of the form

x(n) + p(t)x(n− 2) +H (t,x ) = 0, n ≧ 3
(*)

are studied here, where p(t) 0 and uH(t,u) 0.

It is shown, among other things, that for n even all solutions of () oscillate if H is superlinear, satisfying the usual integral conditions, and u′′ + p(t)u = 0 is nonoscillatory with p(t) “small” and decreasing. The case of n odd is also covered and some of the recent results of Waltman, Heidel are taken as special cases.

Mathematical Subject Classification 2000
Primary: 34C15
Milestones
Received: 25 November 1975
Published: 1 December 1976
Authors
Athanassios G. Kartsatos