Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators
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 eigenvalues μ=μn(r,α) obtained by Ljusternik-Schnirelman theory is studied when the domain Ω0 is deformed continuously. We also consider the cases that Vol(Ωr)→...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000944 |
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| _version_ | 1832556542111514624 |
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| author | Tetsutaro Shibata |
| author_facet | Tetsutaro Shibata |
| author_sort | Tetsutaro Shibata |
| collection | DOAJ |
| description | 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 eigenvalues μ=μn(r,α) obtained by Ljusternik-Schnirelman
theory is studied when the domain Ω0 is deformed continuously. We also consider the cases that
Vol(Ωr)→0,∞ as r→∞. |
| format | Article |
| id | doaj-art-28887e729cca4408a342e266c822d05c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-28887e729cca4408a342e266c822d05c2025-02-03T05:44:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119467968810.1155/S0161171296000944Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operatorsTetsutaro Shibata0Department of Mathematics, Aichi Prefectural University 3-28, Takada-cho, Mizuho-ku, Nagoya 467, JapanWe 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 eigenvalues μ=μn(r,α) obtained by Ljusternik-Schnirelman theory is studied when the domain Ω0 is deformed continuously. We also consider the cases that Vol(Ωr)→0,∞ as r→∞.http://dx.doi.org/10.1155/S0161171296000944Deformation of domainvariational eigenvalues. |
| spellingShingle | Tetsutaro Shibata Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators International Journal of Mathematics and Mathematical Sciences Deformation of domain variational eigenvalues. |
| title | Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators |
| title_full | Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators |
| title_fullStr | Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators |
| title_full_unstemmed | Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators |
| title_short | Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators |
| title_sort | deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators |
| topic | Deformation of domain variational eigenvalues. |
| url | http://dx.doi.org/10.1155/S0161171296000944 |
| work_keys_str_mv | AT tetsutaroshibata deformationofdomainandthelimitofthevariationaleigenvaluesofsemilinearellipticoperators |