On some nonlinear equations with critical exponents

Brezis, Haim;Willem, Michel
(2008) Journal of Functional Analysis — Vol. 255, n° 9, p. 2286-2298 (2008)

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Authors
  • Brezis, Haim
    Author
  • Willem, MichelUCLouvain
    Author
Abstract
Consider the problem {-Delta u + f(|x|/lambda)u/lambda(2) = |u|(4/N-2)u in B-1, u = 0 on partial derivative B-1, where B-1 denotes the open unit ball in R-N, N >= 3 and lambda > 0. Under some general assumptions on f, we prove the existence or the non-existence of radial solutions. We consider also the case when lambda is determined. (C) 2008 Elsevier Inc. All rights reserved.
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Brezis, H., & Willem, M. (2008). On some nonlinear equations with critical exponents. Journal of Functional Analysis, 255(9), 2286-2298. https://doi.org/10.1016/j.jfa.2007.11.022 (Original work published 2008)