The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

Necessary and sufficient condition for oscillations of neutral differential equations

M. R. S. Kulenovića1a2, G. Ladasa1 and A. Meimaridoua1a3

a1 Department of Mathematics, University of Rhode Island, Kingston, R.I. 02881, USA.

a2 Department of Mathematics, University of Sarajevo, Sarajevo 71000, Yugoslavia.

a3 Department of Electrical Engineering, Democritus University of Thrace, Xanthi 67100, Greece.

Abstract

Consider the neutral delay differential equation

S0334270000005452_eqn1

where p xs2208 R, τ ≥ 0, q1 > 0, σ1 ≥ 0, for i = 1, 2, …, k. We prove the following result.

Theorem. A necessary and sufficient condition for the oscillation of all solutions of Eq. (1) is that the characteristic equation

S0334270000005452_eqnU1

has no real roots.

(Received December 13 1985)