Critical points of the Trudinger–Moser trace functional with high energy levels

Deng, Shengbing ; Musso, Monica

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015), p. 59-95 / Harvested from Numdam

Résumé

Let Ω be a bounded domain in $ {\mathbb{R}}^{2}$ with smooth boundary. In this paper we are concerned with the existence of critical points for the supercritical Trudinger–Moser trace functional ∫ ∂Ωe kπ(1+μ)u 2 (0.1) in the set $ \{u\in {H}^{1}(\Omega ):{\int }_{\Omega }({|\mathrm{\nabla }u|}^{2}+{u}^{2})\,dx=1\}$, where $ k⩾1$ is an integer and $ \mu >0$ is a small parameter. For any integer $ k⩾1$ and for any $ \mu >0$ sufficiently small, we prove the existence of a pair of k-peaks constrained critical points of the above problem.

Détail

Publié le : 2015-01-01

MR 3303942 | Zbl 1336.35134

DOI : https://doi.org/10.1016/j.anihpc.2013.10.002

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