  In this paper, we present some suitable distributional identities of the
solutions for nonhomogeneous elliptic equations involving the Hardy-Leray
potentials and study qualitative properties of the solutions to the
corresponding nonhomogeneous problems by the distributional identities. We
address some applications on the nonexistence of some nonhomogeneous problems
with the Hardy-Leray potentials and the nonexistence principle eigenvalue with
some indefinite potentials.
