Boundary Value Problems for the Lyapunov Equation

Abstract

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.