The Nehari manifold for a semilinear elliptic equation involving a sublinear term

K. J. Brown

doi:10.1007/s00526-004-0289-2

The Nehari manifold for a semilinear elliptic equation involving a sublinear term

K. J. Brown

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63 Citations (Scopus)

Abstract

The Nehari manifold for the equation -? u(x) = ? u(x) + b(x) |u(x)|^{?- 2}u(x) for x e ? together with Dirichlet boundary conditions is investigated in the case where 1 < ? < 2. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form t ? J(tu) where J is the Euler functional associated with the equation), we discuss how the Nehari manifold changes as ? changes and show how this is linked to results on bifurcation from infinity which are associated with the problem. © Springer-Verlag 2004.

Original language	English
Pages (from-to)	483-494
Number of pages	12
Journal	Calculus of Variations and Partial Differential Equations
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s00526-004-0289-2
Publication status	Published - Apr 2005

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abstract = "The Nehari manifold for the equation -? u(x) = ? u(x) + b(x) |u(x)|?- 2u(x) for x e ? together with Dirichlet boundary conditions is investigated in the case where 1 < ? < 2. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form t ? J(tu) where J is the Euler functional associated with the equation), we discuss how the Nehari manifold changes as ? changes and show how this is linked to results on bifurcation from infinity which are associated with the problem. {\textcopyright} Springer-Verlag 2004.",

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AB - The Nehari manifold for the equation -? u(x) = ? u(x) + b(x) |u(x)|?- 2u(x) for x e ? together with Dirichlet boundary conditions is investigated in the case where 1 < ? < 2. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form t ? J(tu) where J is the Euler functional associated with the equation), we discuss how the Nehari manifold changes as ? changes and show how this is linked to results on bifurcation from infinity which are associated with the problem. © Springer-Verlag 2004.

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The Nehari manifold for a semilinear elliptic equation involving a sublinear term

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