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

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

Authors:

Affiliation:

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

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

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:

. 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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