Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions
We study the principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem: −Δu(x)=λg(x)u(x), x∈D;(∂u/∂n)(x)+αu(x)=0, x∈∂D, where Δ is the standard Laplace operator, D is a bounded domain with smooth boundary, g:D→ℝ is a smooth function which chang...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007780 |
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| _version_ | 1832561629440507904 |
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| author | G. A. Afrouzi |
| author_facet | G. A. Afrouzi |
| author_sort | G. A. Afrouzi |
| collection | DOAJ |
| description | We study the principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem: −Δu(x)=λg(x)u(x), x∈D;(∂u/∂n)(x)+αu(x)=0, x∈∂D, where Δ is the standard Laplace operator, D is a bounded domain with smooth boundary, g:D→ℝ is a smooth function which changes sign on D and
α∈ℝ. We discuss the relation between α and the principal eigenvalues. |
| format | Article |
| id | doaj-art-46e0be58db724344bcf8ddf5a585bcf2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-46e0be58db724344bcf8ddf5a585bcf22025-02-03T01:24:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01301252910.1155/S0161171202007780Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functionsG. A. Afrouzi0Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, IranWe study the principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem: −Δu(x)=λg(x)u(x), x∈D;(∂u/∂n)(x)+αu(x)=0, x∈∂D, where Δ is the standard Laplace operator, D is a bounded domain with smooth boundary, g:D→ℝ is a smooth function which changes sign on D and α∈ℝ. We discuss the relation between α and the principal eigenvalues.http://dx.doi.org/10.1155/S0161171202007780 |
| spellingShingle | G. A. Afrouzi Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions International Journal of Mathematics and Mathematical Sciences |
| title | Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions |
| title_full | Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions |
| title_fullStr | Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions |
| title_full_unstemmed | Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions |
| title_short | Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions |
| title_sort | boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions |
| url | http://dx.doi.org/10.1155/S0161171202007780 |
| work_keys_str_mv | AT gaafrouzi boundednessandmonotonicityofprincipaleigenvaluesforboundaryvalueproblemswithindefiniteweightfunctions |