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Ukrainian Mathematical Journal

, Volume 71, Issue 6, pp 869–882 | Cite as

Bounded Solutions of the Nonlinear Lyapunov Equation and Homoclinic Chaos

  • O. A. Boichuk
  • O. O. PokutnyiEmail author
Article

We study bounded solutions of a nonlinear Lyapunov-type problem in Banach and Hilbert spaces. Necessary and sufficient conditions for the existence of bounded solutions on the entire axis 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.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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