Critical points of the Trudinger–Moser trace functional with high energy levels
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, pp. 59-95.

Let Ω be a bounded domain in 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 {uH 1 (Ω): Ω (|u| 2 +u 2 )dx=1}, where k1 is an integer and μ>0 is a small parameter. For any integer k1 and for any μ>0 sufficiently small, we prove the existence of a pair of k-peaks constrained critical points of the above problem.

DOI: 10.1016/j.anihpc.2013.10.002
Keywords: Trudinger–Moser trace functional, Reduction methods
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     title = {Critical points of the {Trudinger{\textendash}Moser} trace functional with high energy levels},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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     publisher = {Elsevier},
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Deng, Shengbing; Musso, Monica. Critical points of the Trudinger–Moser trace functional with high energy levels. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, pp. 59-95. doi : 10.1016/j.anihpc.2013.10.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2013.10.002/

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