UNSTABLE NEUTRAL FUNCTIONAL-DIFFERENTIAL EQUATIONS

Let y be the solution of the equation y'(z) = Ay(z) + By(lambda-z) + Cy'(eta-z), z member-of C, where A,B,C,lambda and eta are complex numbers and 0 less-than-or-equal-to \lambda\ < 1, 0 less-than-or-equal-to \eta\ < 1. It is shown that y has exponential order equal to one if A not-equal 0 and if y is not a polynomial; otherwise, y has exponential order equal to zero. In the latter case, y and all of its derivatives are unbounded on any ray.