Ground State for the Schrödinger Operator with the Weighted Hardy Potential
We establish the existence of ground states on ℝ𝑁 for the Laplace operator involving the Hardy-type potential. This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We also obtain a higher integrability property for the princip...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/358087 |
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| _version_ | 1832546623850283008 |
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| author | J. Chabrowski K. Tintarev |
| author_facet | J. Chabrowski K. Tintarev |
| author_sort | J. Chabrowski |
| collection | DOAJ |
| description | We establish the existence of ground states on ℝ𝑁 for the Laplace operator involving the Hardy-type potential. This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We also obtain a higher integrability property for the principal eigenfunction. This is used to examine the behaviour of the principal eigenfunction around 0. |
| format | Article |
| id | doaj-art-ae80b07f924d4315826eac56288dec72 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-ae80b07f924d4315826eac56288dec722025-02-03T06:47:53ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/358087358087Ground State for the Schrödinger Operator with the Weighted Hardy PotentialJ. Chabrowski0K. Tintarev1Department of Mathematics, The University of Queensland, St. Lucia 4072, QLD, AustraliaDepartment of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, SwedenWe establish the existence of ground states on ℝ𝑁 for the Laplace operator involving the Hardy-type potential. This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We also obtain a higher integrability property for the principal eigenfunction. This is used to examine the behaviour of the principal eigenfunction around 0.http://dx.doi.org/10.1155/2011/358087 |
| spellingShingle | J. Chabrowski K. Tintarev Ground State for the Schrödinger Operator with the Weighted Hardy Potential International Journal of Differential Equations |
| title | Ground State for the Schrödinger Operator with the Weighted Hardy Potential |
| title_full | Ground State for the Schrödinger Operator with the Weighted Hardy Potential |
| title_fullStr | Ground State for the Schrödinger Operator with the Weighted Hardy Potential |
| title_full_unstemmed | Ground State for the Schrödinger Operator with the Weighted Hardy Potential |
| title_short | Ground State for the Schrödinger Operator with the Weighted Hardy Potential |
| title_sort | ground state for the schrodinger operator with the weighted hardy potential |
| url | http://dx.doi.org/10.1155/2011/358087 |
| work_keys_str_mv | AT jchabrowski groundstatefortheschrodingeroperatorwiththeweightedhardypotential AT ktintarev groundstatefortheschrodingeroperatorwiththeweightedhardypotential |