  The interplay between a dS black hole and cosmological horizons introduces
distinctive thermodynamic behavior in a dS spacetime (for example the
well-known upper bounds of mass and entropy in Class. Quant. Grav. 37 (2020)
5). Based on this point, we present the Hawking-Page (HP) phase transition of
the four-dimensional dS spacetime with non-linear charge correction when the
effective pressure is fixed, and analyze the effects of different effective
pressures and non-linear charge corrections on HP phase transition. The
evolution of this dS spacetime undergoing the HP phase transition is also
investigated. We find that the existent curve of HP phase transition is a
closed one with two different branches. That means there exist the upper bounds
of the HP temperature and HP pressure, which is completely distinguished with
that in AdS spacetime. And with the decreasing of the distance between two
horizons, the dS spacetime at the coexistent curve of HP phase transition is
going along with different branches. Furthermore we also explore the influence
of charge and non-linear charge correction on the coexistent curve.
