The author considers neutral differential equations of odd order of the form
where , , , , , , and are real constants. It is well-known that a necessary and sufficient condition for oscillation of all solutions of (1) is that the characteristic equation associated with (1) has no real roots. Since this is not easily verifiable, the author’s aim is to obtain sufficient conditions for oscillation of (1) involving the coefficients and the arguments only. A typical result is the following theorem: “Suppose that , , and are positive constants and , , and are nonnegative constants. Let
Then the equation is oscillatory.” At the end of the paper, the author notes that his results are extendable to more general neutral and nonneutral equations.