On the asymptotics of solutions of the Lane-Emden problem for the p-Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the asymptotics of solutions of the Lane-Emden problem for the p-Laplacian

Authors:

Institution:

1. Institut de Mathématique, Université de Mons-Hainaut, Le Pentagone, 6, Avenue du Champ de Mars, B-7000, Mons, Belgium
2. Mathematisches Institut, Universit?t zu K?ln, Weyertal 86-90, D-50931, K?ln, Germany

Abstract:

In this paper we consider the Lane–Emden problem adapted for the p-Laplacian

$\left\{\begin{array}{l} -\Delta_{p}u = \lambda |u|^{q-2}u,\quad {\rm in}\,\Omega,\\ \quad\quad u=0, \quad\quad\quad\quad\,{\rm on}\, \partial \Omega,\end{array}\right.$

where Ω is a bounded domain in $\mathbb{R}^n$ , n ≥ 2, λ > 0 and p < q < p* (with $p^* = \frac{np}{n-p}$ if p < n, and p* = ∞ otherwise). After some recalls about the existence of ground state and least energy nodal solutions, we prove that, when q → p, accumulation points of ground state solutions or of least energy nodal solutions are, up to a “good” scaling, respectively first or second eigenfunctions of −Δ_p. Received: 29 April 2008

Keywords:

" target="_blank"> p-Laplacian energy functional ground state solutions least energy nodal solutions (nodal) Nehari manifold first and second eigenfunctions of − Δ p

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