  As is known, Little-Parks effect concerned with oscillations of the critical
temperature of a superconducting transition was one of the first effects which
suggested the existence of Cooper pairing in conventional superconductors. It
is shown that in high-temperature superconductors (HTSC) the Little-Parks
effect based on bipolaron mechanism which in HTSC is the equivalent of Cooper
pairing can be anomalously high. The results obtained can be used as a new
method for detecting soft phonon modes in nanostructures on the basis of HTSC.
The results can be also used to enhance the critical temperature of a
superconducting transition.
