Multiple positive and 2-nodal symmetric solutions of elliptic problems with critical nonlinearity |
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Authors: | Alfredo Cano |
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Institution: | Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior C.U., 04510 México D.F., Mexico |
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Abstract: | We consider the problem −Δu+a(x)u=f(x)|u|2*−2u in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN, N?4, is the critical Sobolev exponent, and a,f are continuous functions. We assume that Ω, a and f are invariant under the action of a group of orthogonal transformations. We obtain multiplicity results which contain information about the symmetry and symmetry-breaking properties of the solutions, and about their nodal domains. Our results include new multiplicity results for the Brezis-Nirenberg problem −Δu+λu=|u|2*−2u in Ω, u=0 on ∂Ω. |
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Keywords: | 35J65 35J20 |
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