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

2012/09/13 by Weiwei Ao, Juncheng Wei, Ao, Weiwei +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1209.2824

openalex publication_date 2012/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the following singularly perturbed Neumann problem eqnarray* \ve² Δu -u +u^p = 0 in Ω, u>0 in Ω, ∂ u \over ∂ ν=0 on ∂ Ω, eqnarray* where p is subcritical and Ω is a smooth and bounded domain in \Rⁿ with its unit outward normal ν. Lin-Ni-Wei \citeLNW proved that there exists \ve₀ such that for 0

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