We establish sufficient conditions for the bifurcation of solutions of the boundary-value problems for the Lyapunov equation in Hilbert spaces. The cases where the generating equation has or does not have solutions are analyzed. As an example, we consider the problem in the space l2 of sequences with matrices of countable dimensions.
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Translated from Neliniini Kolyvannya, Vol. 20, No. 3, pp. 373–390, July–September, 2017.
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Panasenko, E.V., Pokutnyi, O.O. Bifurcation Conditions for the Solutions of the Lyapunov Equation in a Hilbert Space. J Math Sci 236, 313–332 (2019). https://doi.org/10.1007/s10958-018-4113-5
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DOI: https://doi.org/10.1007/s10958-018-4113-5