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In this paper, second order equations of the form z(t) + A0z(t) + Dz(t) = 0 are studied, where A0 is a uniformly positive operator and A −1/2 0 DA −1/2 0 is a bounded nonnegative operator in a Hilbert space H . This equation is equivalent to the standard first-order equation ẋ(t) = Ax(t) , where A has the domain

Location of the spectrum of operator matrices which are associated to second order equations