Geodesic
Oscillations of Second Order Neutral Equations
Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1301-1314

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Consider the second order neutral differential equation 1 where the coefficients p and q and the deviating arguments τ and σ are real numbers. The characteristic equation of Eq. (1) is 2 The main result in this paper is the following necessary and sufficient condition for all solutions of Eq. (1) to oscillate.THEOREM. The following statements are equivalent: (a) Every solution of Eq. (1) oscillates. (b) Equation (2) has no real roots. 
Ladas, G.; Partheniadis, E. C.; Sficas, Y. G. Oscillations of Second Order Neutral Equations. Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1301-1314. doi: 10.4153/CJM-1988-057-0
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[1] 1. Grammatikopoulos, M. K., Grove, E. A. and Ladas, G., Oscillation and asymptotic behavior of second order neutral differential equations with deviating arguments, Proceedings of the International Conference in Differential Equations, Univ. of Toronto, Canada, July 14–26, 1986. Google Scholar

[2] 2. Ladas, G., Partheniadis, E. C. and Sficas, Y. G., Necessary and sufficient conditions for oscillations of second order neutral equations, J. Math. Anal. Appl. (to appear). Google Scholar | DOI

[3] 3. Ladas, G., Partheniadis, E. C. and Sficas, Y. G., Oscillations of second order neutral equations, Proceedings of Equadiff 87, to be published by Marcel Dekker, Inc. Google Scholar | DOI

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