Symmetry breaking for a class of semilinear elliptic problems
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- by Mythily Ramaswamy and P. N. Srikanth PDF
- Trans. Amer. Math. Soc. 304 (1987), 839-845 Request permission
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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- 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