JournalsrlmVol. 19 , No. 1DOI 10.4171/rlm/508

Entire solutions of autonomous equations on <em><strong>R</strong><sup>n</sup></em> with nontrivial asymptotics

  • Andrea Malchiodi

    Scuola Normale Superiore, Pisa, Italy
Entire solutions of autonomous equations on <em><strong>R</strong><sup>n</sup></em> with nontrivial asymptotics cover

Abstract

We prove existence of a new type of solutions for the semilinear equation \Du+u=up- \D u + u = u^p on Rn\R^n, with 1<p<n+2n21 < 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.