Nonoscillation for Functional Differential Equations of Mixed Type

An example is given to show that the linear autonomous functional differential equation of mixed type ˙x t.qHy1 1 wdm s.xx tqs.s0 may have a nonoscillatory solution in spite of the nonexistence of real roots of its characteristic equation. Under a regularity condition on m at 1, exponential boundedness and asymptotic expansions are obtained for the nonoscillatory solutions