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Generic existence result for an eigenvalue problem with rapidly growing principal operator
Published online by Cambridge University Press: 15 October 2004
Abstract
We consider the eigenvalue problem $$ \begin{array}{l} \displaystyle-{\rm div} (a(|\nabla u |)\nabla u) = \lambda g(x, u) \;\mbox{ in } \Omega u = 0 \;\mbox{ on } \partial\Omega , \end{array} $$ in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all λ > 0 are eigenvalues.
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- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 4 , October 2004 , pp. 677 - 691
- Copyright
- © EDP Sciences, SMAI, 2004
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