Some extensions of the initial value problem for second order evolution equations (Q1101889)

The authors consider second order linear systems of equations in Hilbert space, in the usual variational setting, and with some symmetry conditions imposed upon the operator valued coefficient. They obtain existence and unicity of the solution of the Cauchy problem, this result is an extension (to systems) of a previous work of the first named author [Acta Math. Sci. 4, 81-92 (1984; Zbl 0584.35055)]. The authors obtain also some results on the existence and unicity of the C.P. for a single equation of 2nd order in Hilbert space.