Bounded solutions of the nonlinear Lyapunov equation and homoclinic chaos - Boichuk, О. A.; Pokutnyi, О. О. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
UDC 517.9 The paper is devoted to the investigation of bounded solutions of a nonlinear Lyapunov-type problem in Banach and Hilbertspaces. Necessary and sufficient conditions for the existence of bounded solutions are obtained under the assumption thatthe homogeneous equation admits exponential dichotomy on the semiaxes. Conditions for the existence of homoclinicchaos in nonlinear evolution equations are presented.