Abstract

We consider the problem of finding positive solutions of ?u+?u+uq=0 in a bounded, smooth domain ? in ?3, under zero Dirichlet boundary conditions. Here q is a number close to the critical exponent 5 and 0<?<?1. We analyze the role of Green's function of ?+? in the presence of solutions exhibiting single and multiple bubbling behavior at one point of the domain when either q or ? are regarded as parameters. As a special case of our results, we find that if ?* <?<?1, where ?* is the Brezis-Nirenberg number, i.e., the smallest value of ? for which least energy solutions for q = 5 exist, then this problem is solvable if q > 5 and q - 5 is sufficiently small. © 2004 Elsevier SAS. All rights reserved.