Boundedness of solutions for a second order differential equation with causal operators

摘要

This paper deals with the asymptotic behavior of solutions to the second order functional differential equation X +(Lx)+ grad F (x) = f (t),(0.1) on the half-axis R_+ = [0,∞), with special concern on the boundedness of its solutions. Condition are provided on the data, such that all the solutions of (0.1) are defined on the whole R_+, together with their first derivatives. The basic local existence result is available in [4].