The paper discusses the asymptotic properties of solutions of the scalar functional differential equation of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution which behaves in this way.
We study the asymptotic behavior of the solutions of a differential equation with unbounded delay. The results presented are based on the first Lyapunov method, which is often used to construct solutions of ordinary differential equations in the form of power series. This technique cannot be applied to delayed equations and hence we express the solution as an asymptotic expansion. The existence of a solution is proved by the retract method.
In the paper we study the existence of nonoscillatory solutions of the system , with the property for some . Sufficient conditions for the oscillation of solutions of the system are also proved.
This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as .