Influence of the mass on nodal solutions of nonlinear PDEs

DOI10.1016/S0007-4497(00)00140-8zbMath0997.58019WikidataQ58052282 ScholiaQ58052282MaRDI QIDQ1588726

David Holcman

Publication date: 4 December 2000

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemnodal solutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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• Remarque sur le problème de Yamabe. (Remark on the problem of Yamabe)
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Transformation conforme de la courbure scalaire sur une variété Riemannienne compacte. (Conformal transformation of the scalar curvature on a compact Riemannian manifold)
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Symmetry and related properties via the maximum principle
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• On the proof of the positive mass conjecture in general relativity
• Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire
• Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth
• Best constants in the Sobolev imbedding theorem
• The Yamabe problem

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