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

Manifold Kato 

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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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