Symmetry breaking for a class of semilinear elliptic problems and the bifurcation diagram for a 1-dimensional problem |
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Authors: | Sudhasree Gadam |
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Institution: | 1. School of Mathematics, Univ. of Minnesota, 127 Vincent Hall, 206 Church st. S.E., 55455, Minneapolis, MN, USA
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Abstract: | We study the behaviour of the positive solutions to the Dirichlet problem IR
n
in the unit ball in IR
R
wherep<(N+2)/(N−2) ifN≥3 and λ varies over IR. For a special class of functionsg viz.,g(x)=u
0
p
(x) whereu
0 is the unique positive solution at λ=0, we prove that for certain λ’s nonradial solutions bifurcate from radially symmetric
positive solutions. WhenN=1, we obtain the complete bifurcation diagram for the positive solution curve. |
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Keywords: | 1980 Mathematics Subject classification(1985 Revision)" target="_blank">1980 Mathematics Subject classification(1985 Revision) Primary 35J25 Sec 35P30 |
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