  In this thesis we deal with the specific collective phenomena in condensed
matter - striped-structures formation. Such structures are observed in
different branches of condensed matter physics, like surface physics or physics
of high-temperature superconductors. These quasi-one-dimensional objects appear
in theoretical analyses as well as in computer simulations of different
theoretical models. Here, the main topic of interest is the stability of
striped structures in certain quantum models, where a tendency towards
crystallization competes with a tendency towards phase separation, and some
basic properties of these structures.
