@article{Boichuk_Pokutnyi_2019, title={Bounded solutions of the nonlinear Lyapunov equation
and homoclinic chaos}, volume={71}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1474}, abstractNote={UDC 517.9 <br>
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.}, number={6}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={BoichukО. A. and PokutnyiО. О.}, year={2019}, month={Jun.}, pages={761-773} }