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Ground State for the Schrödinger Operator with the Weighted Hardy Potential

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  • J. Chabrowski
  • K. Tintarev

Abstract

We establish the existence of ground states on â„ ð ‘ 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.

Suggested Citation

  • J. Chabrowski & K. Tintarev, 2011. "Ground State for the Schrödinger Operator with the Weighted Hardy Potential," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-26, September.
    • Handle: RePEc:hin:jnijde:358087
    DOI: 10.1155/2011/358087
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