scholarly journals On a semilinear elliptic eigenvalue problem

1997 ◽  
Vol 67 (3) ◽  
pp. 289-295
Author(s):  
Mario Coclite
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Eigenvalue Problem ◽  
Semilinear Elliptic

On the maximum of solutions for a semilinear elliptic problem

1988 ◽  
Vol 108 (3-4) ◽  
pp. 357-370 ◽  
Author(s):  
Guido Sweers
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Problem ◽  
Dimensional Case ◽  
Bounded Domains ◽  
One Dimensional ◽  
Elliptic Eigenvalue Problem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Right Hand ◽  
The One

SynopsisIn this paper we study some properties of a semilinear elliptic eigenvalue problem with nondefinite right-hand side. In the first part we show that every solution will have its maximum in some specified interval J. If the domain is inside a cone in ℝN with N > 1, then J is strictly smaller than in the one-dimensional case. In the second part we show, for bounded domains, that if the maximum is inside some subinterval of J, then for any eigenvalue there will be at most one solution.

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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