  In this paper, we introduce finite energy classes of quaternionic
plurisubharmonic functions of Cegrell type and study the quaternionic
Monge-Ampere operator on these classes on quaternionic hyperconvex domains of
Hn. We extend the domain of definition of quaternionic Monge-Ampere operator to
some Cegrell classes, the functions of which are not necessarily bounded. We
show that integration by parts and comparison principle are valid on some
classes. Moreover, we use the variational method to solve the quaternionic
Monge-Ampere equations when the right hand side is a positive mea- sure of
finite energy.
