We solve a nonlocal boundary value problem on the half-close interval [1,∞) associated to the differential equation (a(t)|x′|^{α}sgn x′)′+b(t)|x|^{β}sgn x=0, in the the superlinear case α<β. By using a new approach, based on a special energy-type function E, the existence of slowly decaying solutions is examined too.