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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

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topLe, 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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