Abstract
This chapter describes the oscillations of higher-order retarded differential equations (R.D.E) generated by the retarded argument. R.D.E. provides a mathematical model for physical systems in which the rate of change of the system depends upon its past history. Much of the recent literature has been devoted to the extension of known results for ordinary differential equations of R.D.E. In the case n = 2 the derivative of any nonoscillatory solution of is clearly bounded. Therefore, under the conditions, with n = 2, the derivative of any solution of the R.D.E is oscillatory. In this condition, the solutions of equation admit the decomposition S = S0US∼. In addition to the hypotheses of the theorem presented, assuming n = 2k +1 every solution of the equation is oscillatory.
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