An upper bound for the least energy of a sign-changing solution to a zero mass problem

We give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation -Delta u = f(u), u is an element of D-1,D-2(R-N), where N >= 5 and the nonlinearity f is subcritical at infinity and supercritical near the origin. More precisely, we establish the existence of a nonradial sign-changing solution whose energy is smaller that 12c(0) if N = 5, 6 and smaller than 10c(0) if N >= 7, where c(0) is the ground state energy.