Vol. 128, No. 2, 1987
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Oscillatory properties of systems of first order linear delay differential inequalities

K. Gopalsamy
Vol. 128 (1987), No. 2, 299–305
DOI: 10.2140/pjm.1987.128.299
Abstract

Sufficient conditions are obtained for the nonexistence of eventually positive bounded solutions of the system of delay differential inequalities

dxi(t) ∑n dt + aijxj(t− τij) ≤ 0; i = 1,2,...,n j=1

and for the nonexistence of eventually negative bounded solutions of

dxi(t) ∑n ----- + aijxj(t − τij) ≥ 0; i = 1,2,...,n. dt j=1

As a corollary to the above we obtain sufficient conditions for all bounded solutions of

∑n dxi(t) + aijxj(t− τij) = 0; i = 1,2,...,n dt j=1

to be oscillatory.
Mathematical Subject Classification 2000
Primary: 34K15
Secondary: 34A40, 34C10, 34C11
Milestones
Received: 3 December 1985
Published: 1 June 1987
Authors
K. Gopalsamy