An optimal bound on the number of interior spike solutions for Lin-Ni-Takagi problem

Weiwei Ao, Juncheng Wei, Jing Zeng

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…