New classes of entire solutions for semilinear elliptic problems in ℝ<i>ⁿ</i>

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.