International Journal of Differential Equations

Ground State for the Schrödinger Operator with the Weighted Hardy Potential

J. Chabrowski and K. Tintarev

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Abstract

We establish the existence of ground states on N 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.

Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 358087, 26 pages.

Dates
Received: 6 May 2011
Accepted: 17 July 2011
First available in Project Euclid: 25 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485313232

Digital Object Identifier
doi:10.1155/2011/358087

Zentralblatt MATH identifier
1234.35157

Citation

Chabrowski, J.; Tintarev, K. Ground State for the Schrödinger Operator with the Weighted Hardy Potential. Int. J. Differ. Equ. 2011 (2011), Article ID 358087, 26 pages. doi:10.1155/2011/358087. https://projecteuclid.org/euclid.ijde/1485313232


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