  We describe boundary effects in superconducting systems with
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting instability, using
Bogoliubov-de-Gennes and Ginzburg-Landau (GL) formalisms. First, we show that
in dimensions larger than one the standard GL functional formalism for FFLO
superconductors is unbounded from below. This is demonstrated by finding
solutions with zero Laplacian terms near boundaries. We generalize the GL
formalism for these systems by retaining higher order terms. Next, we
demonstrate that a cuboid sample of a superconductor with imbalanced fermions
at a mean-field level has a sequence of the phase transitions. At low
temperatures it forms Larkin-Ovchinnikov state in the bulk but has a different
modulation pattern close to the boundaries. When temperature is increased the
first phase transition occurs when the bulk of the material becomes normal
while the faces remain superconducting. The second transition occurs at higher
temperature where the system retains superconductivity on the edges. The third
transition is associated with the loss of edge superconductivity while
retaining superconducting gap in the vertices. We obtain the same sequence of
phase transition by numerically solving the Bogoliubov-de Gennes model.
