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

Vy Khoi Le

ESAIM: Control, Optimisation and Calculus of Variations (2004)

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

Abstract

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We consider the eigenvalue problem - div ( a ( | ∇ u | ) ∇ u ) = λ g ( x , u ) in Ω u = 0 on ∂ Ω , 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 (2004): 677-691. <http://eudml.org/doc/244618>.

@article{Le2004,
abstract = {We consider the eigenvalue problem\[\hspace*\{-11.38109pt\} \begin\{array\}\{l\} -\{\rm div\} (a(|\nabla u |)\nabla u) = \lambda g(x, u) \;\mbox\{ in \} \Omega \\ u = 0 \;\mbox\{ on \} \partial \Omega , \end\{array\} \]in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all $\lambda &gt;0$ 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},
language = {eng},
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/244618},
volume = {10},
year = {2004},
}

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
PY - 2004
PB - EDP-Sciences
VL - 10
IS - 4
SP - 677
EP - 691
AB - We consider the eigenvalue problem\[\hspace*{-11.38109pt} \begin{array}{l} -{\rm div} (a(|\nabla u |)\nabla u) = \lambda g(x, u) \;\mbox{ in } \Omega \\ u = 0 \;\mbox{ on } \partial \Omega , \end{array} \]in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all $\lambda &gt;0$ are eigenvalues.
LA - eng
KW - quasilinear elliptic equation; generic existence; variational inequality; rapidly growing operator
UR - http://eudml.org/doc/244618
ER -

References

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