  Basing on self-consistent solution of non-linear GL-equations, the phase
boundary is found, which divides the regions of I- and II-order phase
transitions of a superconducting cylinder in magnetic field to normal state.
This boundary is a complicated function of the parameters (m,R,kappa) (m is the
vorticity, R is the cylinder radius, kappa is the GL-parameter), which does not
coincide with the simple phase boundary kappa=1/\sqrt{2}, dividing the regions
of I- and II-order phase transitions in infinite (open) superconducting
systems.
