  Precise measurements of the time-dependent intensity of the low energy ($<50$
GeV) galactic cosmic rays are fundamental to test and improve the models which
describe their propagation inside the heliosphere. Especially, data spanning
different solar activity periods, i.e. from minimum to maximum, are needed to
achieve comprehensive understanding of such physical phenomenon. The minimum
phase between the 23$^{rd}$ and the 24$^{th}$ solar cycles was peculiarly long,
extending up to the beginning of 2010 and followed by the maximum phase,
reached during early 2014. In this paper, we present proton differential
spectra measured from January 2010 to February 2014 by the PAMELA experiment.
For the first time the galactic cosmic ray proton intensity was studied over a
wide energy range (0.08-50 GeV) by a single apparatus from a minimum to a
maximum period of solar activity. The large statistics allowed the time
variation to be investigated on a nearly monthly basis. Data were compared and
interpreted in the context of a state-of-the-art three-dimensional model
describing the galactic cosmic rays propagation through the heliosphere.
