Existence of multi-peak solutions for p-Laplace problems in ℝN

In this paper we consider the p-Laplace problem \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ - {\varepsilon ^p}{\Delta _p}u + V\left( x \right){u^{p - 1}} = {u^{q - 1}},u{\text{ > }}0$\end{document} in RN where 2 ≤ p < N, ε > 0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p{\text{ < }}q{\text{ < }}p* = \frac{{Np}}{{N - p}}$\end{document}. V is a non-negative function satisfying certain conditions and ε is a small parameter. We obtain the existence of solutions concentrated near set consisting of disjoint components of zero set of V under certain assumptions on V when ε > 0 is small.