# Generic existence result for an eigenvalue problem with rapidly growing principal operator

• Volume: 10, Issue: 4, page 677-691
• ISSN: 1292-8119

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## Abstract

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We consider the eigenvalue problem $\begin{array}{c}-\mathrm{div}\left(a\left(|\nabla u|\right)\nabla u\right)=\lambda g\left(x,u\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{4.0pt}{0ex}}\text{in}\phantom{\rule{4.0pt}{0ex}}\Omega u=0\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{4.0pt}{0ex}}\text{on}\phantom{\rule{4.0pt}{0ex}}\partial \Omega ,\hfill \end{array}$ 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.

## How to cite

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Le, Vy Khoi. "Generic existence result for an eigenvalue problem with rapidly growing principal operator." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2010): 677-691. <http://eudml.org/doc/90751>.

@article{Le2010,
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. },
author = {Le, Vy Khoi},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Quasilinear elliptic equation; generic existence; variational inequality; rapidly growing operator.; quasilinear elliptic equation; rapidly growing operator},
language = {eng},
month = {3},
number = {4},
pages = {677-691},
publisher = {EDP Sciences},
title = {Generic existence result for an eigenvalue problem with rapidly growing principal operator},
url = {http://eudml.org/doc/90751},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Le, Vy Khoi
TI - Generic existence result for an eigenvalue problem with rapidly growing principal operator
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 4
SP - 677
EP - 691
AB - 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.
LA - eng
KW - Quasilinear elliptic equation; generic existence; variational inequality; rapidly growing operator.; quasilinear elliptic equation; rapidly growing operator
UR - http://eudml.org/doc/90751
ER -

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