New classes of entire solutions for semilinear elliptic problems in $ℝ^n$

Abstract

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.