A necessary and sufficient condition for the oscillation of higher-order neutral equations with several delays (Q1192374)

The present paper contains necessary and sufficient conditions under which all solutions of higher order neutral equations with several delays oscillate. These conditions are equivalent to the absence of real roots of their characteristic equations. The result is obtained by means of methods contained in a paper of \textit{M. K. Grammatikopoulos}, \textit{Y. G. Sficas} and \textit{I. P. Stavroulakis} [J. Differ. Equations 76, No. 2, 294-311 (1988; Zbl 0669.34069)], and a result quite similar to the result of the present paper is also obtained by two of these authors and \textit{S. J. Bilchev} [J. Aust. Math. Soc., Ser. A 52, No. 2, 261-284 (1992; Zbl 0754.34071)].