A Uniqueness Result for a Singular Nonlinear Eigenvalue Problem

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Mathematics (HMC)

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We consider the positive solutions to singular boundary-value problems of the form

where λ > 0, β ∈ (0,1) and Ω is a bounded domain in ℝ N , N ≥ 1, with smooth boundary ∂Ω. Here, we assume that f: [0, ∞) → (0, ∞) is a C 1 non-decreasing function and f(s)/s β is decreasing for s large. We establish the uniqueness of the positive solution when λ is large.

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