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

✍ Scribed by Juncheng Wei; Shusen Yan

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 310 KB
• Volume: 88
• Category: Article
• ISSN: 0021-7824
• DOI: 10.1016/j.matpur.2007.07.001

✦ Synopsis

We consider the following problem,

where μ > 0 is a large parameter, Ω is a bounded domain in R N , 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.