Vol. 52, No. 1, 1974

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Oscillatory properties of a delay differential equation of even order

Raymond D. Terry

Vol. 52 (1974), No. 1, 269–282

A classification of nonoscillatory solutions according to the sign properties of their derivatives i6 introduced for a general nonlinear delay differential equation of order 2n. It is seen that there are n types of positive solutions of this equation. An intermediate Riccatti transformation is employed to obtain integral criteria for the nonexistence of such solutions and for the oscillation of all solutions. Analysis of the Taylor Remainder gives rise to a summability condition which is used to investigate the asymptotic behavior of a class of solutions. The major results are then shown to be special cases of a more general result based on the direct method of Lyapunov.

Mathematical Subject Classification
Primary: 34K15
Received: 18 December 1972
Revised: 23 July 1973
Published: 1 May 1974
Raymond D. Terry