Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 6, p. 1027-1047

We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem $-\Delta u={|u|}^{{2}^{⁎}-2-ϵ}u\phantom{\rule{1em}{0ex}}\text{in}\phantom{\rule{4pt}{0ex}}\Omega ,\phantom{\rule{2em}{0ex}}u=0\phantom{\rule{1em}{0ex}}\text{on}\phantom{\rule{4pt}{0ex}}\partial \Omega ,$ where Ω is a smooth bounded domain in ${ℝ}^{N}$, $N⩾3$, ${2}^{⁎}=\frac{2N}{N-2}$ and $ϵ>0$ is a small parameter. In particular we prove that if Ω is convex and satisfies a certain symmetry, then a nodal four-bubble solution exists with two positive and two negative bubbles.

DOI : https://doi.org/10.1016/j.anihpc.2013.01.001
Classification:  35B40,  35J20,  35J65
Keywords: Slightly subcritical problem, Sign-changing solutions, Finite-dimensional reduction, Max–min argument
@article{AIHPC_2013__30_6_1027_0,
author = {Bartsch, Thomas and D'Aprile, Teresa and Pistoia, Angela},
title = {Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {30},
number = {6},
year = {2013},
pages = {1027-1047},
doi = {10.1016/j.anihpc.2013.01.001},
zbl = {1288.35212},
mrnumber = {3132415},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2013__30_6_1027_0}
}

Bartsch, Thomas; DʼAprile, Teresa; Pistoia, Angela. Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 6, pp. 1027-1047. doi : 10.1016/j.anihpc.2013.01.001. http://www.numdam.org/item/AIHPC_2013__30_6_1027_0/

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