Existence of positive solutions for the Hénon equation involving critical Sobolev terms

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Abstract

Let N ≥ 3, 2* = 2 N / (N - 2) and Ω ⊂ RN be a bounded domain with a smooth boundary ∂Ω and 0 ∈ Ω. Our purpose in this paper is to consider the existence of solutions of Hénon equation:{(- Δ u (x) = | x |α | u (x) |2* - 1, in Ω,; u > 0, in Ω,; u = 0, on ∂ Ω,) where α > 0. © 2009 Elsevier Inc. All rights reserved.

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Hirano, N. (2009). Existence of positive solutions for the Hénon equation involving critical Sobolev terms. Journal of Differential Equations, 247(5), 1311–1333. https://doi.org/10.1016/j.jde.2009.06.008

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