Multi-peak solutions for the Hénon equation with slightly subcritical growth

We study the Dirichlet problem for the Hénon equation\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\{ \begin{array}{ll} -\Delta u=|x|^\alpha u^{\frac{N+2}{N-2}-\varepsilon} &\hbox{in } \Omega,\\ u > 0 &\hbox{in } \Omega,\\ u=0 &\hbox{on } \partial\Omega,\\ \end{array}\right. $$\end{document} where Ω is the unit ball in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}^N$$\end{document}, with N ≥ 3, the power α is positive and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document} is a small positive parameter. We prove that for every integer k ≥ 1 the above problem has a solution which blows up at k different points of ∂Ω as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document} goes to zero. We also show that the ground state solution (which blows up at one point) is unique.