Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains |
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Authors: | Amandine Aftalion Filomena Pacella |
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Affiliation: | 1. Laboratoire Jacques-Louis Lions, B.C.187, université Paris 6, 175, rue du Chevaleret, 75013 Paris, France;2. Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy |
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Abstract: | We study the qualitative properties of sign changing solutions of the Dirichlet problem in Ω, on ?Ω, where Ω is a ball or an annulus and f is a function with . We prove that any radial sign changing solution has a Morse index bigger or equal to and give sufficient conditions for the nodal surface of a solution to intersect the boundary. In particular, we prove that any least energy nodal solution is non radial and its nodal surface touches the boundary. To cite this article: A. Aftalion, F. Pacella, C. R. Acad. Sci. Paris, Ser. I 339 (2004). |
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