JournalsrlmVol. 19, No. 1pp. 65–72

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
Download PDF

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.

Cite this article

Andrea Malchiodi, Entire solutions of autonomous equations on <em><strong>R</strong><sup>n</sup></em> with nontrivial asymptotics. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 1, pp. 65–72

DOI 10.4171/RLM/508