Some new entire solutions of semilinear elliptic equations on R^n

We prove existence of a new type of positive solutions of the semilinear equation − \Delta u + u = u^p on Rn, where 1<p< n+2/n−2 . These solutions are bounded, but do not tend to zero at infinity. Indeed, they decay to zero away from three half-lines with a common origin, and their asymptotic profile is periodic along these half-lines