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

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Abstract.

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

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, UK

    K. J. Brown

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  1. K. J. Brown
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Additional information

Received: 8 December 2003, Accepted: 10 May 2004, Published online: 16 July 2004

Mathematics Subject Classification (2000):

35J20, 35J25

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Brown, K.J. The Nehari manifold for a semilinear elliptic equation involving a sublinear term. Calc. Var. 22, 483–494 (2004). https://doi.org/10.1007/s00526-004-0289-2

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  • DOI: https://doi.org/10.1007/s00526-004-0289-2

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