COMPARISON METHODS FOR EIGENVALUES OF SEMILINEAR ELLIPTIC OPERATORS

1988 ◽  
pp. 119-124
Author(s):  
R. CHIAPPINELLI
Keyword(s):  
Elliptic Operators ◽  
Semilinear Elliptic ◽  
Comparison Methods

scholarly journals Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators

1996 ◽  
Vol 19 (4) ◽  
pp. 679-688 ◽  
Author(s):  
Tetsutaro Shibata
Keyword(s):  
Asymptotic Behavior ◽  
Eigenvalue Problem ◽  
Elliptic Operators ◽  
Elliptic Eigenvalue Problem ◽  
Semilinear Elliptic

We consider the semilinear elliptic eigenvalue problem{Lu+f(x,u)=μu  in  Ωr(r≥0),u=0  on  ∂Ωr.The asymptotic behavior of the variational eigenvaluesμ=μn(r,α)obtained by Ljusternik-Schnirelman theory is studied when the domainΩ0is deformed continuously. We also consider the cases thatVol(Ωr)→0,∞asr→∞.

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