Abstract
We study boundary-value problems for a Lyapunov-type equation in the space Lp.(I, ℒ(ℋ)): Necessary and sufficient conditions for the solvability of the corresponding boundary-value problem are established both in linear and nonlinear cases. The solutions of the linear boundary-value problem are constructed by using the generalized Green operator. It is proposed to find the approximate solutions of the nonlinear equation by using iterative Newton–Kantorovich-type algorithms.
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