In this paper, we prove that the Brezis-Nirenberg problem: -Δu = |u|p-1u + εuinΩ,u = 0on∂Ω, where Ω is a symmetric bounded smooth domain in RN, N ≥ 7 and p = N+2 N-2, has a solution with the shape of a tower of two bubbles with alternate signs, centered at the center of symmetry of the domain, for all ε > 0 sufficiently small.
Sign-changing tower of bubbles for the Brezis-Nirenberg problem
Vaira G.
2016-01-01
Abstract
In this paper, we prove that the Brezis-Nirenberg problem: -Δu = |u|p-1u + εuinΩ,u = 0on∂Ω, where Ω is a symmetric bounded smooth domain in RN, N ≥ 7 and p = N+2 N-2, has a solution with the shape of a tower of two bubbles with alternate signs, centered at the center of symmetry of the domain, for all ε > 0 sufficiently small.File in questo prodotto:
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