An optimal bound on the number of interior spike solutions for Lin-Ni-Takagi problem
Weiwei Ao, Juncheng Wei, Jing Zeng · arXiv (Cornell University) · 2012
We consider the following singularly perturbed Neumann problem {eqnarray*} \ve^2 Δu -u +u^p = 0 \quad {in} \quad Ω, \quad u>0 \quad {in} \quad Ω, \quad {\partial u \over \partial ν}=0 \quad {on} \quad \partial Ω, {eqnarray*} where $p$ is subcritical and $Ω$ is a smooth and bounded domain in $\R^n$ with its unit outward normal $ν$. Lin-Ni-Wei \cite{LNW} proved that there exists $\ve_0$ such that for $0