On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity

J. Chabrowski; Shusen Yan

Colloquium Mathematicae, Tome 91 (2002), p. 141-150 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the Neumann problem for the equation $- Δ u - λ u = {Q (x) | u |}^{2 * - 2} u$ , u ∈ H¹(Ω), where Q is a positive and continuous coefficient on Ω̅ and λ is a parameter between two consecutive eigenvalues $λ_{k - 1}$ and $λ_{k}$ . Applying a min-max principle based on topological linking we prove the existence of a solution.

Publié le : 2002-01-01

Zbl 1090.35074

EUDML-ID : urn:eudml:doc:284757

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     title = {On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity},
     journal = {Colloquium Mathematicae},
     volume = {91},
     year = {2002},
     pages = {141-150},
     zbl = {1090.35074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-10}
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J. Chabrowski; Shusen Yan. On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity. Colloquium Mathematicae, Tome 91 (2002) pp. 141-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-10/