Existence of quadratic Lyapunov functionals for equations with unbounded operators in Hilbert space (Q1358065)

For a linear differential equation with a bounded operator in a Hilbert space the exponential stability is equivalent with the existence of a positive definite quadratic Lyapunov functional, which solves the Lyapunov equation. This is not the case, in general, for equations with unbounded operators. This article gives conditions on the unbounded operator guaranteeing the above mentioned equivalence.