Abstract
In this paper we are concerned with the following Neumann problem where ϵ is a small positive parameter, f is an odd superlinear and subcritical nonlinearity, Ω is a bounded 𝒞4 domain in ℝ N without any symmetry assumption. Denoting by ℋ(P), P ∈ ∂Ω, the mean curvature of the boundary, it is known that this problem has positive multiple boundary peak solutions with each peak concentrating at a different critical point of ℋ or with all the peaks approaching a local minimum point of ℋ. In this paper we assume that ℋ has a nondegenerate maximum point P 0 ∈ ∂Ω and we show that there exists a ℓ-peak solution with mixed positive and negative peaks concentrating at P 0.
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