Nonoscillation for functional differential equations of mixed type (Q1570201)

It is considered the linear autonomous functional-differential equation \[ \dot x(t)+ \int^1_{-1} (d\mu(s)) x(t+ s)= 0 \] which is of mixed (retarted/advanced) type. An example shows that such equations may be nonoscillatory in spite of the existence of the real roots of the characteristic equation. Exponential estimates and boundedness are analyzed. It is shown that nonoscillatory solutions may be bounded even without exponential bounds for all solutions.