Bounded solutions of the nonlinear Lyapunov equation and homoclinic chaos
The paper is devoted to the investigation of bounded solutions of a nonlinear Lyapunov-type problem in Banach and Hilbert spaces. Necessary and sufficient conditions for the existence of bounded solutions are obtained under the assumption that the homogeneous equation admits exponential dichotomy on the semiaxes. Conditions for the existence of homoclinic chaos in nonlinear evolution equations are presented.
How to Cite
BoichukО. A., and PokutnyiО. О. “Bounded Solutions of the Nonlinear Lyapunov equation and Homoclinic Chaos”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 6, June 2019, pp. 761-73, http://umj.imath.kiev.ua/index.php/umj/article/view/1474.