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

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We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem

-Δu=|u| 2 ⁎ -2-ϵ uinΩ,u=0on∂Ω,
where Ω is a smooth bounded domain in ℝ N , N⩾3, 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 : 10.1016/j.anihpc.2013.01.001
Classification : 35B40, 35J20, 35J65
Keywords: Slightly subcritical problem, Sign-changing solutions, Finite-dimensional reduction, Max–min argument 
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     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},
     pages = {1027--1047},
     publisher = {Elsevier},
     volume = {30},
     number = {6},
     year = {2013},
     doi = {10.1016/j.anihpc.2013.01.001},
     mrnumber = {3132415},
     zbl = {1288.35212},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2013.01.001/}
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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, Tome 30 (2013) no. 6, pp. 1027-1047. doi: 10.1016/j.anihpc.2013.01.001

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