Geodesic
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

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We consider the eigenvalue problem

- div (a(|∇u|)∇u)=λg(x,u)inΩu=0on∂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.

DOI : 10.1051/cocv:2004027
Classification : 35J65, 35J20, 35J60, 47J30, 49J40, 58E05
Keywords: 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},
     volume = {10},
     number = {4},
     year = {2004},
     doi = {10.1051/cocv:2004027},
     mrnumber = {2111088},
     zbl = {1118.35011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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

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