Abstract
In this paper, we consider the problem: −Δu=N(N−2)u p−ɛ, u>0 on Ω; u=0 on ∂Ω, where Ω is a smooth and bounded domain inR N, N≥3, p=\(\frac{{N + 2}}{{N - 2}}\), and ε>0. We prove a conjecture of H. Brezis and L.A. Peletier about the asymptotic behaviour of solutions of this problem which are minimizing for the Sobolev inequality as ε goes to zero. We give similar results concerning the related problem: −Δu=N(N−2)up+εu, u>0 on Ω; u=0 on ∂Ω, for N is larger than 4.
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Rey, O. Proof of two conjectures of H. Brezis and L.A. Peletier. Manuscripta Math 65, 19–37 (1989). https://doi.org/10.1007/BF01168364
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DOI: https://doi.org/10.1007/BF01168364