Generic existence result for an eigenvalue problem with rapidly growing principal operator
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 677-691.

We consider the eigenvalue problem

 $\phantom{\rule{-11.38109pt}{0ex}}\begin{array}{c}-\mathrm{div}\left(a\left(|\nabla u|\right)\nabla u\right)=\lambda g\left(x,u\right)\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{4pt}{0ex}}\text{in}\phantom{\rule{4pt}{0ex}}\Omega \hfill \\ u=0\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{4pt}{0ex}}\text{on}\phantom{\rule{4pt}{0ex}}\partial \Omega ,\hfill \end{array}$
in the case where the principal operator has rapid growth. By using a variational approach, we show that under certain conditions, almost all $\lambda >0$ are eigenvalues.

DOI : https://doi.org/10.1051/cocv:2004027
Classification : 35J65,  35J20,  35J60,  47J30,  49J40,  58E05
Mots clés : quasilinear elliptic equation, generic existence, variational inequality, rapidly growing operator
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author = {Le, Vy Khoi},
title = {Generic existence result for an eigenvalue problem with rapidly growing principal operator},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {677--691},
publisher = {EDP-Sciences},
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doi = {10.1051/cocv:2004027},
zbl = {1118.35011},
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url = {http://www.numdam.org/articles/10.1051/cocv:2004027/}
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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, Tome 10 (2004) no. 4, pp. 677-691. doi : 10.1051/cocv:2004027. http://www.numdam.org/articles/10.1051/cocv:2004027/

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