Boundary-Value Problems for the Lyapunov Equation in Banach Spaces

Panasenko, E. V.; Pokutnyi, O. O.

doi:10.1007/s10958-017-3356-x

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2018

2024

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Cited by 7 publications

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“…Розглянемо випадок, коли множина значень оператора L не є замкненою. Оскiльки оператор L має (X, R(L)) узагальнений L допустимий пiдпростiр, то для просторiв L(B 1 ), B 2 справедливий розклад (26).…”

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Boundary Value Problems for the Lyapunov Equation

Pokutnyi

2023

JNAM

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The boundary value problems for the Lyapunov equation in the resonant (irregular) case in Banach and Hilbert spaces, when the solution of the equation does not exist for all right-hand sides and its uniqueness may be violated, have been investigated. The conditions for bifurcation and branching of solutions in linear and nonlinear cases, including with a moving right end of the segment on which the corresponding boundary value problem is considered, are found.

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