Abstract

We present a finite-dimensional reduction for a supercritical exponent PDE. We reduce the existence of a solution of the problem − Δ u = K | u | 4 ∕ ( n − 2 ) + e u in Ω (with e > 0 ) , u = 0 on ∂ Ω , to finding a critical point of a function defined in some set V⊂ℝN×ℝN×ΩN.

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