We study a weakly coupled supercritical elliptic system of the formWe assume that Ω is invariant under the action of a group G of linear isometries, R N is the sum F ⊕ F ⊥ of G-invariant linear subspaces, and x2 is the projection onto F ⊥ of the point x ∈ Ω.Then, under some assumptions on Ω and F , we establish the existence of infinitely many fully nontrivial G-invariant solutions to this system for p ≥ 2 * up to some value which depends on the symmetries and on γ. Our results apply, in particular, to the system with pure power nonlinearity (γ = 0), and yield new existence and multiplicity results for the supercritical Hénon-type equation −∆w = |x2| γ |w| p−2 w in Ω, w = 0 on ∂Ω.
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