# Asymptotic profiles for the Kirchhoff equation

### TOKIO MATSUYAMA

Tokai University, Kanagawa, Japan

## Abstract

The first aim of this paper is to find asymptotic profiles for Kirchhoff equation. More precisely, it will be shown that there exists a small amplitude solution which is not asymptotically free. The second aim is to prove the existence of scattering states for the small amplitude solutions with data belonging to $H^{\sigma(p),p}\times H^{\sigma(p)-1,p}$, where $\sigma(p)= n(\frac{2}{p}-1)+1$, $p\in [1,\frac{2(n-1)}{n+1})$ and $n \ge 4$.

## Cite this article

TOKIO MATSUYAMA, Asymptotic profiles for the Kirchhoff equation. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 4, pp. 377–395

DOI 10.4171/RLM/475