naa a22 4500 510781438 CHVBK 20180411083248.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11854-013-0039-5 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0039-5 Miyamoto Yasuhito Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-Ku, 223-8522, Yokohama, Japan aut Symmetry breaking bifurcation from solutions concentrating on the equator of $$\mathbb{S}^N$$ [Elektronische Daten] [Yasuhito Miyamoto] We are concerned with the elliptic problem $${\varepsilon ^2}{\Delta _{{S^n}}}u - u + {u^p} = 0{\text{ in }}{S^n},u > 0{\text{ in }}{S^n}$$ , where $${\Delta _{{S^n}}}$$ is the Laplace-Beltrami operator on $$\mathbb{S}^n : = \left\{ {x \in \mathbb{R}^{n + 1} ;\left\| x \right\| = 1} \right\}\left( {n \geqslant 3} \right)$$ , and p ⩾ 2. We construct a smooth branch C of solutions concentrating on the equator S n ∩ {x n+1 = 0}. Using the Crandall-Rabinowitz bifurcation theorem, we show that C has infinitely many bifurcation points from which continua of nonradial solutions emanate. In applying the bifurcation theorem, we verify the transversality condition directly. Hebrew University Magnes Press, 2013 Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 353-381 0021-7670 121:1<353 2013 121 11854 https://doi.org/10.1007/s11854-013-0039-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0039-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Miyamoto Yasuhito Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-Ku, 223-8522, Yokohama, Japan aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 353-381 0021-7670 121:1<353 2013 121 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer