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Nehari manifold

  • Michel Willem
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 24)

Abstract

Assume that φ ∈ C1(X, ℝ) is such that φ′(0) = 0. A necessary condition for uX to be a critical point of φ is that \(\langle \varphi \prime(u),u\rangle \, = 0\). This condition defines the Nehari manifold
$$N\,: = \{ u \in X\,:\langle \varphi \prime(u),u\rangle \, = \,0,u \ne 0\}$$
.

Keywords

Unit Sphere Nonnegative Solution Small Ball Symmetric Domain Radial Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser 1996

Authors and Affiliations

  • Michel Willem
    • 1
  1. 1.Département de MathématiqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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