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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Symmetry breaking for a class of semilinear elliptic problems


Authors: Mythily Ramaswamy and P. N. Srikanth
Journal: Trans. Amer. Math. Soc. 304 (1987), 839-845
MSC: Primary 35J65; Secondary 35B32, 58E07
DOI: https://doi.org/10.1090/S0002-9947-1987-0911098-4
MathSciNet review: 911098
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Abstract: We study positive solutions of the Dirichlet problem for $ - \Delta u = {u^p} - \lambda $, $ p > 1$, $ \lambda > 0$, on the unit ball $ \Omega $. We show that there exists a positive solution $ ({u_0},\,{\lambda _0})$ of this problem which satisfies in addition $ \partial {u_0}/\partial n = 0$ on $ \partial \Omega $. We prove also that at $ ({u_0},\,{\lambda _0})$, the symmetry breaks, i.e. asymmetric solutions bifurcate from the positive radial solutions.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0911098-4
Article copyright: © Copyright 1987 American Mathematical Society