  The possibility of the superconducting transition in the two-dimensional
repulsive Hubbard model is studied using the ladder approximation of the strong
coupling diagram technique. The $t$-$U$ and $t$-$t'$-$t''$-$U$ models are
considered in the regime of strong correlations, for the on-site Coulomb
repulsion $U=8t$, in the range of temperatures $0.02t\lesssim T\lesssim 0.3t$.
To avoid the influence of the phase separation and size effects the
calculations are performed in an infinite crystal, in the part of the phase
diagram without inhomogeneities, for the electron concentration $\bar{n}
=0.92$. Solutions of the Eliashberg equation for singlet and triplet pairing,
which are transformed according to one-dimensional representations of the
lattice point group $D_4$, are considered. For both models and all considered
symmetries, eigenvalues of the Eliashberg equation are less than unity and
demonstrate no upward trend with decreasing temperature. This result points to
the absence of superconductivity in the Hubbard model in the strong-coupling
regime. We discuss the reason for the small eigenvalue of the Eliashberg
equation in the case of the singlet $d_{x^2-y^2}$ pairing.
