In this paper, we consider the Cauchy problem: formula math. The stationary problem for (ECP) is the famous Choquard-Pekar problem, and it has a unique positive solution u(x) as long as p(x) is radial, continuous in R 3 , p(x) ≥ a > 0, and lim |x|→ ∞p(x) = p > 0. In this paper, we prove that if the initial data 0 ≤ u 0 (x) ≤ (=) u(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t → ∞, if u 0 (x) ≥ (=) u (x), then the solution u(x, t) blows up in finite time.