Boundary-value problems for the Lyapunov equation. І - Boichuk, O.; Panasenko, Ye.; Pokutnyi, O. (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 517.9We study boundary-value problems for the Lyapunov operator-differential  equation. By using  the theory of Moore–Penrose pseudoinverse operators  and its development, we establish conditions for the existence of generalized solutions and propose algorithms for their construction.