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The problem of Cooper instability is studied by implementing theKohn-Luttinger mechanism in the framework of the Shubin-Vonsowsky model takinginto account the intersite Coulomb interactions within the first and secondcoordination spheres. It is shown that the Kohn-Luttinger renormalization forthe effective interaction in the second-order terms of perturbation theory, aswell as the inclusion of intersite hoppings in the second and thirdcoordination spheres, significantly affects the interplay between thesuperconducting phases with $d_{xy}$-, $p$-, $s$-, and $d_{x^2-y^2}$-wavesymmetries of the order parameter.

Effect of long-range interactions on the Kohn-Luttinger mechanism of the Cooper instability in the Shubin-Vonsowsky model