A Singularly Perturbed Linear Eigenvalue Problem in C1 Domains

where ν is the outward unit normal vector on ∂Ω; ν exists a.e. for Lipschitz domains. The goal of this paper is to understand the asymptotic behavior of Λ(γ) as γ → ∞ when ∂Ω ∈ C1. Since Λ(γ) → ∞ when γ → ∞, (2) can be viewed as a singularly perturbed linear eigenvalue problem. The asymptotic behavior of Λ(γ) was first studied by Lacey, Ockendon and Sabina in [3], where they investigated some reaction-diffusion model in which distributed nonlinear absorption mechanisms compete with nonlinear boundary sources. In order to describe the long time behaviors of solutions to this reaction-diffusion model, it is important to understand the asymptotic behavior of Λ(γ) as γ → ∞ (see [3] and the references therein). Among other things, Lacey, Ockendon and Sabina showed in [3] that