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

Tetsutaro Shibata

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-10

Abstract:

We consider the semilinear elliptic eigenvalue problem { L u + f ( x , u ) = μ u in Ω r ( r ≥ 0 ) , u = 0 on ∂ Ω r . The asymptotic behavior of the variational eigenvalues μ = μ n ( r , α ) obtained by Ljusternik-Schnirelman theory is studied when the domain Ω 0 is deformed continuously. We also consider the cases that V o l ( Ω r ) → 0 , ∞ as r → ∞ .

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:431709

DOI: 10.1155/S0161171296000944

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