Least Energy Nodal Solutions of the Brezis-nirenberg Problem in Dimension N=5

Roselli, Paolo;Willem, Michel
(2009) Communications in Contemporary Mathematics — Vol. 11, n° 1, p. 59-69 (2009)

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We prove the existence of (a pair of) least energy sign changing solutions of {-Delta u = vertical bar u vertical bar(2*-2)u + lambda u in Omega u = 0 on partial derivative Omega when Omega is a bounded domain in R-N, N = 5 and. is slightly smaller than lambda(1), the first eigenvalue of -Delta with homogeneous Dirichlet boundary conditions on Omega.
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Roselli, P., & Willem, M. (2009). Least Energy Nodal Solutions of the Brezis-nirenberg Problem in Dimension N=5. Communications in Contemporary Mathematics, 11(1), 59-69. https://doi.org/10.1142/S0219199709003314 (Original work published 2009)