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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

Vy Khoi Le
Vy Khoi Le*
Affiliation:
Department of Mathematics and Statistics, University of Missouri–Rolla, MO 65401, USA; vy@umr.edu.
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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.

Keywords

Quasilinear elliptic equationgeneric existencevariational inequalityrapidly growing operator.
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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