  Here we present an analysis of the evolution of Majorana corner modes
realizing in a higher-order topological superconductor (HOTSC) on a square
lattice under the influence of local Coulomb repulsion. The HOTSC spectral
properties were considered in two regimes: when the intensities of many-body
interactions are either weak or strong. The weak regime was studied using the
mean-field approximation with self-consistent solutions carried out both in the
uniform case and taking into account of the boundary of the finite
square-shaped system. It is shown that in the uniform case the topologically
nontrivial phase on the phase diagram is widened by the Coulomb repulsion. The
boundary effect, resulting in an inhomogeneous spatial distribution of the
correlators, leads to the appearance of the crossover from the symmetric
spin-independent solution to the spin-dependent one characterized by a
spontaneously broken symmetry. In the former the corner states have energies
that are determined by the overlap of the excitation wave functions localized
at the different corners. In the latter the corner excitation energy is defined
by the Coulomb repulsion intensity with a quadratic law. The crossover is a
finite size effect, i.e. the larger the system the lesser the critical value of
the Coulomb repulsion. In the strong repulsion regime we derive the effective
HOTSC Hamiltonian in the atomic representation and found a rich variety of
interactions induced by virtual processes between the lower and upper Hubbard
subbands. It is shown that Majorana corner modes still can be realized in the
limit of the infinite repulsion. Although the boundaries of the topologically
nontrivial phase are strongly renormalized by Hubbard corrections.
