Z

global behavior of solutions to the nonlinear Klein-Gordon equation on R1+2: uu+ u+ f(u) = 0; u: R1+2! R; (1) with the nonlinearity f of the Sobolev critical growth order for juj! 1: f(u) = (e4u 2 1 4u2)u; (2) where we subtract the cubic term in order to avoid another critical problem at juj! 0. The equation has the conserved energy E(u) = E0(u; t) + F (u(t)); E0(u; t):