BUBBLE TOWER SOLUTIONS OF SLIGHTLY SUPERCRITICAL ELLIPTIC EQUATIONS AND APPLICATION IN SYMMETRIC DOMAINS

(Communicated by Aim Sciences) Abstract. We construct solutions of the semilinear elliptic problem{ ∆u+ |u|p−1u+ ε 12 f = 0 in Ω u = ε 1 2 g on ∂Ω in a bounded smooth domain Ω ⊂ RN (N ≥ 3), when the exponent p is super-critical and close enough to N+2 N−2. As p → N+2N−2, the solutions have multiple blow up at finitely many points which are the critical points of a function whose definition involves Green’s function. As applications, we will give some existence results, in particular, when Ω are symmetric domains perforated with the small hole and when f = 0 and g = 0