Functional-Differential Equations with Compressed Arguments and Polynomial Coefficients: Asymptotics of the Solutions

Functional-differential equations with linearly compressed arguments and polynomial coefficients are considered. We prove, under some mild restrictions on the coefficients, that each solution y(t) of such an equation, satisfying estimate |y(t)| ≤ C exp{γ In2 |t|} (t → ∞), where 0 < γ < γ̃, is polynomial.