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 -Δu=|u| 2 -2-ϵ uinΩ,u=0onΩ, where Ω is a smooth bounded domain in N , N3, 2 =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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