Abstract
We consider the following problem, − Δ u + μ u = u 2 ∗ − 1 , u > 0 in Ω , ∂ u ∂ n = 0 on ∂ Ω , where μ > 0 is a large parameter, Ω is a bounded domain in R N , N ⩾ 3 and 2 ∗ = 2 N / ( N − 2 ) . Let H ( P ) be the mean curvature function of the boundary. Assuming that H ( P ) has a local minimum point with positive minimum, then for any integer k, the above problem has a k-boundary peaks solution. As a consequence, we show that if Ω is strictly convex, then the above problem has arbitrarily many solutions, provided that μ is large.
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