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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.

Non-radial solutions with orthogonal subgroup invariance for semilinear Dirichlet problems