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.
|Number of pages||19|
|Journal||Journal of Differential Equations|
|Publication status||Published - 20 Sept 2003|
- Indefinite weight functions
- Nehari manifold
- Variational methods