Abstract
The Nehari manifold for the equation -?u(x) = ?a(x)u(x) + b(x) u(x)v-1u(x) for x?O together with Dirichlet boundary conditions is investigated. 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 existence and non-existence results for positive solutions of the equation are linked to properties of the manifold. © 2003 Elsevier Science (USA). All rights reserved.
Original language | English |
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Pages (from-to) | 481-499 |
Number of pages | 19 |
Journal | Journal of Differential Equations |
Volume | 193 |
Issue number | 2 |
DOIs | |
Publication status | Published - 20 Sept 2003 |
Keywords
- Indefinite weight functions
- Nehari manifold
- Variational methods