Symmetry breaking for a class of semilinear elliptic problems

P.N. Srikanth

doi:10.1016/s0294-1449(16)30301-8

JournalsaihpcVol. 7, No. 2pp. 107–112

Symmetry breaking for a class of semilinear elliptic problems

P.N. Srikanth
Tata Institute of Fundamental Research, P.O. Box 1234, Bangalore-560 012, India

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Abstract

In this article we consider the problem

- Δ u u u = u^{p} + λ u = 0 > 0 in Ω on \partial Ω (P_{λ})

where $Ω$ is an annulus and $p > 1$ . We prove there is always a break of symmetry along the branch of radial solutions if the thickness of $Ω$ is sufficiently small.

Résumé

Dans cet article, nous considérons le problème

- Δ u u u = u^{p} + λ u, = 0 > 0, dans Ω, sur \partial Ω (P_{λ})

ou $Ω$ est un anneau et $p > 1$ . Nous montrons qu’il y a toujours une casse de symétrie dans la branche des solutions radiales, si l’épaisseur de $Ω$ est suffisamment petite.

Cite this article

P.N. Srikanth, Symmetry breaking for a class of semilinear elliptic problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 2, pp. 107–112

DOI 10.1016/S0294-1449(16)30301-8