Of concern is the existence, uniqueness and asymptotic behavior of solutions to an initial value problem for the second-order equation
in a Hilbert space H. Here denotes the norm in H, K: is linear monotone, A is a given linear unbounded operator of H, and M is a real function on . The author extends earlier results by P. Biler [ibid. 10, 839-842 (1986; Zbl 0611.35057)], and E. H. Brito [ibid. 8, 1489-1496 (1984; Zbl 0524.35026); ibid. 11, 125-137 (1987; Zbl 0613.34013)].