Representation and boundary values of solutions of homogeneous second- order operator-differential equation (Q1090826)

The operator equation \(y''(t)+p(A)y'(t)+q(A)y(t)=0\) is considered on the ray (0,\(\infty)\) in a separable Hilbert space, A is a non-negative selfadjoint operator, p(\(\lambda)\), q(\(\lambda)\) are polynomials. A representation of the strong solutions is given. It is a natural generalization of the previous results in both simple and double root cases. Some other properties of these solutions are also considered.