Multi-layer radial solutions for a supercritical neumann problem

Abstract

In this paper we study the Neumann problem\begin{equation*}\begin{cases}-Δu+u=u^p \& \text{ in }B\_1 \\u \textgreater{} 0, \& \text{ in }B\_1 \\\partial\_νu=0 \& \text{ on } \partial B\_1,\end{cases}\end{equation*}and we show the existence of multiple-layer radial solutions as $p\rightarrow+\infty$.