caa a22 4500 605495882 CHVBK 20210128100533.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10231-013-0368-0 doi (NATIONALLICENCE)springer-10.1007/s10231-013-0368-0 On the second minimax level of the scalar field equation and symmetry breaking [Elektronische Daten] [Kanishka Perera, Cyril Tintarev] We study the second minimax level $$\lambda _2$$ λ 2 of the eigenvalue problem for the scalar field equation in $$\mathbb{R }^N$$ R N . We prove the existence of an eigenfunction at the level $$\lambda _2$$ λ 2 when the potential near infinity approaches the constant level from below no faster than $$\mathrm{{e}}^{- \varepsilon \, |x|}$$ e - ε | x | . We also consider questions about the nodality of eigenfunctions at this level and establish symmetry breaking at the levels $$2,\ldots ,N$$ 2 , ... , N . The Author(s), 2013 Scalar field equation nationallicence Minimax methods nationallicence Concentration compactness nationallicence Symmetry breaking nationallicence Perera Kanishka Department of Mathematical Sciences, Florida Institute of Technology, 32901, Melbourne, FL, USA aut Tintarev Cyril Department of Mathematics, Uppsala University, 75106, Uppsala, Sweden aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 131-144 0373-3114 194:1<131 2015 194 10231 https://doi.org/10.1007/s10231-013-0368-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0368-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Perera Kanishka Department of Mathematical Sciences, Florida Institute of Technology, 32901, Melbourne, FL, USA aut NATIONALLICENCE 700 1- Tintarev Cyril Department of Mathematics, Uppsala University, 75106, Uppsala, Sweden aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 131-144 0373-3114 194:1<131 2015 194 10231