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Uniqueness for a class p-Laplacian problems when a parameter is large

Alreshidi B., Hai D. D.

Opuscula Mathematica

2024

Vol. 44, no. 1

5--17

We prove uniqueness of positive solutions for the problem−Δpu = λf(u) in Ω, u = 0 on ∂Ω, where 1 < p < 2 and p is close to 2, Ω is bounded domain in Rn with smooth boundary ∂Ω, f : [0,∞) → [0,∞) with f(z) ∼ zβ at ∞ for some β ∈ (0, 1), and λ is a large parameter. The monotonicity assumption on f is not required even for u large.