LAUSR

Abstract Inspired from the constructive method of Davilla et al. [10] , with new ingredients, we extend their existence results to dimensions 7 ≤ n ≤ 9 concerning the following Henon type problem { − Δ u = K | u | p − 1 − e u in Ω , u = 0 on ∂ Ω , where Ω is a smooth bounded domain in R n , e is a positive real parameter, p + 1 = 2 n / ( n − 2 ) is the critical Sobolev exponent and the function K ∈ C 2 ( Ω ‾ ) is positive satisfying condition (1.1) .