Entire solutions of autonomous equations on $\mathbb R^n$ with nontrivial asymptotics
Andrea Malchiodi · Rendiconti Lincei Matematica e Applicazioni · 2008
We prove existence of a new type of solutions for the semilinear equation - \Delta u + u = u^p on \R^n , with 1 < p < \frac{n+2}{n-2} . These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.