Non-radial solutions with orthogonal subgroup invariance for semilinear Dirichlet problems
Keywords
Semilinear elliptic equation, group invariant solution, non-radial solution, variational methodAbstract
A semilinear elliptic equation, $-\Delta u=\lambda f(u)$, is studied in a ball with the Dirichlet boundary condition. For a closed subgroup $G$ of the orthogonal group, it is proved that the number of non-radial $G$ invariant solutions diverges to infinity as $\lambda$ tends to $\infty$ if $G$ is not transitive on the unit sphere.Downloads
Published
2003-03-01
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KAJIKIYA, Ryuji. Non-radial solutions with orthogonal subgroup invariance for semilinear Dirichlet problems. Topological Methods in Nonlinear Analysis. Online. 1 March 2003. Vol. 21, no. 1, pp. 41 - 51. [Accessed 23 September 2024].
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