Autonomous nonlinear boundary-value problems for the Lyapunov equation in Hilbert space - Bihun, D. S.; Pokutnyi, O. O; Panasenko, E. V. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 517.9We investigate boundary value problems for the Lyapunov equation in the Hilbert space in the case where the corresponding problem is defined on an interval that depends on a parameter $ε$. We obtain necessary and sufficient conditions for the existence of generalized solutions of the problem.