  In this paper, a parabolic type Kirchhoff equation and its stationary
counterpart are considered. For the evolution problem, the precise decay rates
of the weak solution and of the corresponding energy functional are derived.
For the stationary problem, a ground-state solution is obtained by applying
Lagrange multiplier method. Moreover, the asymptotic behaviors of the general
global solutions are also described. These results extend some recent ones
obtained in [Threshold results for the existence of global and blow-up
solutions to Kirchhoff equations with arbitrary initial energy, Computers and
Mathematics with Applications, 75(2018), 3283-3297] by Han and Li.
