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In this paper, we present some suitable distributional identities of thesolutions for nonhomogeneous elliptic equations involving the Hardy-Leraypotentials and study qualitative properties of the solutions to thecorresponding nonhomogeneous problems by the distributional identities. Weaddress some applications on the nonexistence of some nonhomogeneous problemswith the Hardy-Leray potentials and the nonexistence principle eigenvalue withsome indefinite potentials.

On nonhomogeneous elliptic equations with the Hardy-Leray potentials