Critical points of the Trudinger–Moser trace functional with high energy levels
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 1, p. 59-95
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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.
@article{AIHPC_2015__32_1_59_0,
     author = {Deng, Shengbing and Musso, Monica},
     title = {Critical points of the Trudinger--Moser trace functional with high energy levels},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {1},
     year = {2015},
     pages = {59-95},
     doi = {10.1016/j.anihpc.2013.10.002},
     zbl = {1336.35134},
     mrnumber = {3303942},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_1_59_0}
}
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, Tome 32 (2015) no. 1, pp. 59-95. doi : 10.1016/j.anihpc.2013.10.002. http://www.numdam.org/item/AIHPC_2015__32_1_59_0/

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