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

Parini, Enea; Grumiau, Christopher

Parini, Enea; Grumiau, Christopher (2008), On the asymptotics of solutions of the Lane-Emden problem for the p -Laplacian, Archiv der Mathematik, 91, 4, p. 354-365. http://dx.doi.org/10.1007/s00013-008-2854-y

Type

Article accepté pour publication ou publié

Date

2008

Journal name

Archiv der Mathematik

Volume

Number

Publisher

Springer

Pages

354-365

Abstract (EN)

In this paper we consider the Lane–Emden problem adapted for the p-Laplacian {(-∆_p u=λ|u|^(q-2),in Ω, u=0, in ∂Ω )┤ where Ω is a bounded domain in Rn, n ≥ 2, λ > 0 and p < q < p* (with p=npn−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 .

Subjects / Keywords

first and second eigenfunctions of −Δ p; (nodal) Nehari manifold; least energy nodal solutions; ground state solutions; energy functional; p-Laplacian