The goal of this paper is to describe some new results concerning entire solutions of semilinear elliptic equations in ℝ_n_ with non trivial asymptotic behavior at infinity. We describe in particular the (focusing, subcritical) nonlinear Schrödinger equation and the Allen-Cahn equation, which enjoy some common features but also present rather di¤erent aspects.
Cite this article
Andrea Malchiodi, New classes of entire solutions for semilinear elliptic problems in ℝ<i><sup>n</sup></i>. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 1, pp. 33–45DOI 10.4171/RLM/559