Triplet $p$-wave superconductivity in low-density extended Hubbard model with Coulomb repulsion

We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density ($n_{\mathrm{el}} \to 0$) on simple cubic (square) lattice. We show that in a realistic strong-coupling case $U\gg V\gg W$ ($U$ and $V$ are the onsite and the intersite Coulomb repulsions, $W$ the bandwidth) the main SC instability corresponds to the $p$-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction $V=0$.