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

Abstract

We consider the following problem, [**EQUATION**] 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.