Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 2, Pages 195-200

Bound and periodic solutions of the Riccati equation in Banach space

A. Ya. Dorogovtsev and T. A. Petrova

Kiev University, Mechanics and Mathematics Department, Vladimirskaya 64, Kiev-17 252125, Ukraine

Received 1 June 1994; Revised 1 January 1995

Copyright © 1995 A. Ya. Dorogovtsev and T. A. Petrova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic) solutions of this equation with a stationary (periodic) process in the right side.