  We study the modulations of the superconducting order parameter in the
vicinity of edges, magnetic and non-magnetic impurities by self-consistently
solving the gap equations of a system with competing interactions in the Cooper
channel. It is shown that the presence or absence of Friedel-like oscillations
of the superconducting order parameter crucially depends on its symmetry and
can, hence, be used to obtain information about the symmetry properties of the
condensate. Furthermore, the appearance of competing order parameters at
inhomogeneities is discussed. We show that this can lead to the presence of a
topologically trivial region close to the boundary of a system that is
topologically nontrivial in its bulk. The resulting shift in position of the
Majorana bound states is demonstrated to significantly affect its signatures in
Josephson-junction experiments. We discuss Josephson scanning tunneling
microscopy as a probe to resolve the Friedel-like oscillations as well as the
spatial texture of competing s-wave superconductivity and Majorana bound states
in the vicinity of the edge of the system.
