Arbitrary many boundary peak solutions for an elliptic Neumann problem with critical growth

AbstractWe consider the following problem,−Δu+μu=u2∗−1,u>0inΩ,∂u∂n=0on∂Ω, where μ>0 is a large parameter, Ω is a bounded domain in RN, N⩾3 and 2∗=2N/(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